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

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

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

prove

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

True

Solution steps

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

Use the basic trigonometric identity:

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

\Rightarrow True

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

cos (θ - \frac{π}{2}) = sin (θ)

csc (x) \cdot cos (x) = cot (x)

cot (a) + tan (a) = 2 csc (2 a)

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