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

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

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

prove

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

True

Solution steps

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

Manipulating right side

- 1 - (cot (x))^{2}

Simplify

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

Rewrite using trig identities

- 1 - cot^{2} (x)

Use the Pythagorean identity:

1 + cot^{2} (x) = csc^{2} (x)

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

= - csc^{2} (x)

= - csc^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1}{csc ( θ )} = - cos (θ)

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

sin (\frac{π}{6} + x) + cos (\frac{π}{3} + x) = cos (x)

1 + tan^{2} (θ) = \frac{1}{cos ( θ )}

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