Is 2cos(x)tan(x)csc(x)=2 ?

The answer to whether 2cos(x)tan(x)csc(x)=2 is True

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prove 2cos(x)tan(x)csc(x)=2

prove

2 cos (x) tan (x) csc (x) = 2

True

Solution steps

2 cos (x) tan (x) csc (x) = 2

Manipulating left side

2 cos (x) tan (x) csc (x)

Express with sin, cos

2 cos (x) csc (x) tan (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

2 cos (x) \frac{1}{sin ( x )} \cdot \frac{sin ( x )}{cos ( x )}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

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

Cancel the common factor:

sin (x)

= \frac{1 \cdot 2 cos ( x )}{cos ( x )}

Cancel the common factor:

cos (x)

= 1 \cdot 2

Multiply the numbers:

1 \cdot 2 = 2

= 2

= 2

= 2

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (y) - cot^{2} (\frac{π}{2} - y) = 1

sin (\frac{π}{3} + x) - sin (\frac{π}{3} - x) = sin (x)

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

tan (x) (csc (x) - sin (x)) = cos (x)

tan (x) (sin (x) + cot (x) cos (x)) = sec (x)