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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

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

\frac{1}{tan ( x )} = cot (x)

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

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

tan (x) \cdot sin (x) + cos (x) = sec (x)

cos (θ) + cos (θ) tan^{2} (θ) = sec (θ)

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