Is 1/(1+cot^2(x))=sin^2(x) ?

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

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prove 1/(1+cot^2(x))=sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{1 + cot ^{2} ( x )}

Express with sin, cos

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

Rewrite using trig identities

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sec (θ) \cdot sin (θ) = tan (θ)

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

sin (θ) = cos (\frac{π}{2} - θ)

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

4 sin^{2} (x) = 3 - 4 sin (x)

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