Is csc^2(x)= 1/(sin^2(x)) ?

The answer to whether csc^2(x)= 1/(sin^2(x)) is True

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prove csc^2(x)= 1/(sin^2(x))

prove

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

True

Solution steps

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

Manipulating left side

csc^{2} (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

(sec^{2} (θ) - 1) cos^{2} (θ) = sin^{2} (θ)

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

cos^{2} (β) - sin^{2} (β) = 2 cos^{2} (β) - 1

(1 - cos (β)) (1 + cos (β)) = \frac{1}{csc ^{2} ( β )}

\frac{cot ( θ ) sec ( θ )}{csc ( θ )} = 1

Is csc^2(x)= 1/(sin^2(x)) ?
The answer to whether csc^2(x)= 1/(sin^2(x)) is True