Is tan(x)(1-csc^2(x))=-cot(x) ?

The answer to whether tan(x)(1-csc^2(x))=-cot(x) is True

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prove tan(x)(1-csc^2(x))=-cot(x)

prove

tan (x) (1 - csc^{2} (x)) = - cot (x)

True

Solution steps

tan (x) (1 - csc^{2} (x)) = - cot (x)

Manipulating left side

tan (x) (1 - csc^{2} (x))

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= - cot (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{9}{tan ( x )} + \frac{9}{cot ( x )} = 9 tan (x) + 9 cot (x)

sin (2 x) cos (2 x) = 4 sin (x) cos (x)

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

\frac{1}{cos ( θ ) sin ( θ )} = sec (θ) csc (θ)

Is tan(x)(1-csc^2(x))=-cot(x) ?
The answer to whether tan(x)(1-csc^2(x))=-cot(x) is True