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受欢迎的代数 >

化简 (cos(x)+sec(x))^2+sin^2(x)-tan^2(x)+3

解答

化简

(cos (x) + sec (x))^{2} + sin^{2} (x) - tan^{2} (x) + 3

解答

7

求解步骤

(cos (x) + sec (x))^{2} + sin^{2} (x) - tan^{2} (x) + 3

展开

(cos (x) + sec (x))^{2} : cos^{2} (x) + 2 cos (x) sec (x) + sec^{2} (x)

= cos^{2} (x) + 2 cos (x) sec (x) + sec^{2} (x) + sin^{2} (x) - tan^{2} (x) + 3

使用毕达哥拉斯恒等式:

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

= sec^{2} (x) + 2 cos (x) sec (x) - tan^{2} (x) + 3 + 1

数字相加:

3 + 1 = 4

= sec^{2} (x) + 2 cos (x) sec (x) - tan^{2} (x) + 4

使用毕达哥拉斯恒等式:

sec^{2} (x) = tan^{2} (x) + 1

sec^{2} (x) - tan^{2} (x) = 1

= 2 cos (x) sec (x) + 4 + 1

数字相加:

4 + 1 = 5

= 2 cos (x) sec (x) + 5

sec (x) cos (x) = 1

= 5 + 2 \cdot 1

数字相乘:

2 \cdot 1 = 2

= 5 + 2

数字相加:

5 + 2 = 7

= 7

流行的例子

展开 (1/2-(sqrt(3))/2 i)^{16}

e x p an d (\frac{1}{2} - \frac{3}{2} i)^{16}

展开 (x^{1/2}+2)^2

e x p an d (x^{\frac{1}{2}} + 2)^{2}

展开 ((e^2+1)(e+1)(e-1))/(2e^2)

e x p an d \frac{( e ^{2} + 1 ) ( e + 1 ) ( e - 1 )}{2 e ^{2}}

展开 1/(3(s+2))

e x p an d \frac{1}{3 ( s + 2 )}

化简 (x-sqrt(3))^2(x-sqrt(7))

s im pl i f y (x - 3)^{2} (x - 7)