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인기 있는 >

tan(pi/2-x)+2tan(pi/2+x)=1

해법

tan (\frac{π}{2} - x) + 2 tan (\frac{π}{2} + x) = 1

해법

x = \frac{3 π}{4} + πn

+1

도

x = 13 5^{\circ} + 18 0^{\circ} n

솔루션 단계

tan (\frac{π}{2} - x) + 2 tan (\frac{π}{2} + x) = 1

삼각성을 사용하여 다시 쓰기

tan (\frac{π}{2} - x) + 2 tan (\frac{π}{2} + x) = 1

삼각성을 사용하여 다시 쓰기

tan (\frac{π}{2} - x)

기본 삼각형 항등식 사용:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( \frac{π}{2} - x )}{cos ( \frac{π}{2} - x )}

각도 차이 식별 사용:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= \frac{sin ( \frac{π}{2} ) cos ( x ) - cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} - x )}

각도 차이 식별 사용:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= \frac{sin ( \frac{π}{2} ) cos ( x ) - cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} ) cos ( x ) + sin ( \frac{π}{2} ) sin ( x )}

\frac{sin ( \frac{π}{2} ) cos ( x ) - cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} ) cos ( x ) + sin ( \frac{π}{2} ) sin ( x )}

단순화하세요:

\frac{cos ( x )}{sin ( x )}

\frac{sin ( \frac{π}{2} ) cos ( x ) - cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} ) cos ( x ) + sin ( \frac{π}{2} ) sin ( x )}

sin (\frac{π}{2}) cos (x) - cos (\frac{π}{2}) sin (x) = cos (x)

sin (\frac{π}{2}) cos (x) - cos (\frac{π}{2}) sin (x)

sin (\frac{π}{2}) cos (x) = cos (x)

sin (\frac{π}{2}) cos (x)

sin (\frac{π}{2})

단순화하세요:

1

sin (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{2}) = 1

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 \cdot cos (x)

곱하다:

1 \cdot cos (x) = cos (x)

= cos (x)

cos (\frac{π}{2}) sin (x) = 0

cos (\frac{π}{2}) sin (x)

cos (\frac{π}{2})

단순화하세요:

0

cos (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{2}) = 0

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0 \cdot sin (x)

규칙 적용

0 \cdot a = 0

= 0

= cos (x) - 0

cos (x) - 0 = cos (x)

= cos (x)

= \frac{cos ( x )}{cos ( \frac{π}{2} ) cos ( x ) + sin ( \frac{π}{2} ) sin ( x )}

cos (\frac{π}{2}) cos (x) + sin (\frac{π}{2}) sin (x) = sin (x)

cos (\frac{π}{2}) cos (x) + sin (\frac{π}{2}) sin (x)

cos (\frac{π}{2}) cos (x) = 0

cos (\frac{π}{2}) cos (x)

cos (\frac{π}{2})

단순화하세요:

0

cos (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{2}) = 0

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0 \cdot cos (x)

규칙 적용

0 \cdot a = 0

= 0

sin (\frac{π}{2}) sin (x) = sin (x)

sin (\frac{π}{2}) sin (x)

sin (\frac{π}{2})

단순화하세요:

1

sin (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{2}) = 1

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 \cdot sin (x)

곱하다:

1 \cdot sin (x) = sin (x)

= sin (x)

= 0 + sin (x)

0 + sin (x) = sin (x)

= sin (x)

= \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )}

기본 삼각형 항등식 사용:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( \frac{π}{2} + x )}{cos ( \frac{π}{2} + x )}

앵글섬식별사용:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= \frac{sin ( \frac{π}{2} ) cos ( x ) + cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} + x )}

앵글섬식별사용:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= \frac{sin ( \frac{π}{2} ) cos ( x ) + cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} ) cos ( x ) - sin ( \frac{π}{2} ) sin ( x )}

\frac{sin ( \frac{π}{2} ) cos ( x ) + cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} ) cos ( x ) - sin ( \frac{π}{2} ) sin ( x )}

단순화하세요:

- \frac{cos ( x )}{sin ( x )}

\frac{sin ( \frac{π}{2} ) cos ( x ) + cos ( \frac{π}{2} ) sin ( x )}{cos ( \frac{π}{2} ) cos ( x ) - sin ( \frac{π}{2} ) sin ( x )}

sin (\frac{π}{2}) cos (x) + cos (\frac{π}{2}) sin (x) = cos (x)

sin (\frac{π}{2}) cos (x) + cos (\frac{π}{2}) sin (x)

sin (\frac{π}{2}) cos (x) = cos (x)

sin (\frac{π}{2}) cos (x)

sin (\frac{π}{2})

단순화하세요:

1

sin (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{2}) = 1

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 \cdot cos (x)

곱하다:

1 \cdot cos (x) = cos (x)

= cos (x)

cos (\frac{π}{2}) sin (x) = 0

cos (\frac{π}{2}) sin (x)

cos (\frac{π}{2})

단순화하세요:

0

cos (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{2}) = 0

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0 \cdot sin (x)

규칙 적용

0 \cdot a = 0

= 0

= cos (x) + 0

cos (x) + 0 = cos (x)

= cos (x)

= \frac{cos ( x )}{cos ( \frac{π}{2} ) cos ( x ) - sin ( \frac{π}{2} ) sin ( x )}

cos (\frac{π}{2}) cos (x) - sin (\frac{π}{2}) sin (x) = - sin (x)

cos (\frac{π}{2}) cos (x) - sin (\frac{π}{2}) sin (x)

cos (\frac{π}{2}) cos (x) = 0

cos (\frac{π}{2}) cos (x)

cos (\frac{π}{2})

단순화하세요:

0

cos (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

cos (\frac{π}{2}) = 0

cos (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0 \cdot cos (x)

규칙 적용

0 \cdot a = 0

= 0

sin (\frac{π}{2}) sin (x) = sin (x)

sin (\frac{π}{2}) sin (x)

sin (\frac{π}{2})

단순화하세요:

1

sin (\frac{π}{2})

다음과 같은 사소한 아이덴티티 사용:

sin (\frac{π}{2}) = 1

sin (x)

주기율표

2 πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 \cdot sin (x)

곱하다:

1 \cdot sin (x) = sin (x)

= sin (x)

= 0 - sin (x)

0 - sin (x) = - sin (x)

= - sin (x)

= \frac{cos ( x )}{- sin ( x )}

분수 규칙 적용:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{cos ( x )}{sin ( x )}

= - \frac{cos ( x )}{sin ( x )}

\frac{cos ( x )}{sin ( x )} + 2 (- \frac{cos ( x )}{sin ( x )}) = 1

\frac{cos ( x )}{sin ( x )} + 2 (- \frac{cos ( x )}{sin ( x )})

단순화하세요:

- \frac{cos ( x )}{sin ( x )}

\frac{cos ( x )}{sin ( x )} + 2 (- \frac{cos ( x )}{sin ( x )})

괄호 제거:

(- a) = - a

= \frac{cos ( x )}{sin ( x )} - 2 \cdot \frac{cos ( x )}{sin ( x )}

유사 요소 추가:

\frac{cos ( x )}{sin ( x )} - 2 \cdot \frac{cos ( x )}{sin ( x )} = - \frac{cos ( x )}{sin ( x )}

= - \frac{cos ( x )}{sin ( x )}

- \frac{cos ( x )}{sin ( x )} = 1

- \frac{cos ( x )}{sin ( x )} = 1

빼다

1

양쪽에서

- \frac{cos ( x )}{sin ( x )} - 1 = 0

- \frac{cos ( x )}{sin ( x )} - 1

단순화하세요:

\frac{- cos ( x ) - sin ( x )}{sin ( x )}

- \frac{cos ( x )}{sin ( x )} - 1

요소를 분수로 변환:

1 = \frac{1 sin ( x )}{sin ( x )}

= - \frac{cos ( x )}{sin ( x )} - \frac{1 \cdot sin ( x )}{sin ( x )}

분모가 같기 때문에, 분수를 합친다:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- cos ( x ) - 1 \cdot sin ( x )}{sin ( x )}

곱하다:

1 \cdot sin (x) = sin (x)

= \frac{- cos ( x ) - sin ( x )}{sin ( x )}

\frac{- cos ( x ) - sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (x) - sin (x) = 0

삼각성을 사용하여 다시 쓰기

- cos (x) - sin (x) = 0

cos (x), cos (x) \neq = 0

양쪽을 다음으로 나눕니다

\frac{- cos ( x ) - sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

단순화

- 1 - \frac{sin ( x )}{cos ( x )} = 0

기본 삼각형 항등식 사용:

\frac{sin ( x )}{cos ( x )} = tan (x)

- 1 - tan (x) = 0

- 1 - tan (x) = 0

1

를 오른쪽으로 이동

- 1 - tan (x) = 0

더하다

1

양쪽으로

- 1 - tan (x) + 1 = 0 + 1

단순화

- tan (x) = 1

- tan (x) = 1

양쪽을 다음으로 나눕니다

- 1

- tan (x) = 1

양쪽을 다음으로 나눕니다

- 1

\frac{- tan ( x )}{- 1} = \frac{1}{- 1}

단순화

tan (x) = - 1

tan (x) = - 1

일반 솔루션

tan (x) = - 1

tan (x)

주기율표

πn

주기:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

그래프

인기 있는 예

(11.0994)/(cos(x))=(3.5355)/(sin(x))

\frac{11.0994}{cos ( x )} = \frac{3.5355}{sin ( x )}

((sec(x))/(cos(x)))^2=tan^2(x)

(\frac{sec ( x )}{cos ( x )})^{2} = tan^{2} (x)

sin(x/2)-cos(x/2)=0

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

2sin^2(x/3)=1,-pi<= ,x<= pi

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

cos^2(x)+sin^2(x)=sin(x)+1/2

cos^{2} (x) + sin^{2} (x) = sin (x) + \frac{1}{2}