Is tan(x)=-cot(2x)+csc(2x) ?

The answer to whether tan(x)=-cot(2x)+csc(2x) is True

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prove tan(x)=-cot(2x)+csc(2x)

prove

tan (x) = - cot (2 x) + csc (2 x)

True

Solution steps

tan (x) = - cot (2 x) + csc (2 x)

Manipulating right side

- cot (2 x) + csc (2 x)

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{π}{6}) = sin (\frac{π}{6} + \frac{π}{2})

cos^{4} (\frac{- 3 π}{4}) = cos^{4} (\frac{π}{4})

cos (6 x) + cos (2 x) = 2 cos (4 x) cos (2 x)

cos (x) + cot (x) + sin (x) = csc (x)

sin (\frac{π}{4}) + cos (\frac{π}{4}) = 2

Is tan(x)=-cot(2x)+csc(2x) ?
The answer to whether tan(x)=-cot(2x)+csc(2x) is True