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

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 - csc^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

- cos^{2} (x) csc^{2} (x)

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

We showed that the two sides could take the same form

\Rightarrow True

sec (θ) = sin (θ) (tan (θ) + cot (θ))

\frac{csc ^{2} ( A )}{1 + tan ^{2} ( A )} = cot^{2} (A)

sin (3 a) = 3 sin (a) - 4 sin^{3} (a)

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

\frac{1}{tan ( θ ) csc ( θ )} = cos (θ)

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