Is 1+cot^2(θ)= 1/(sin^2(θ)) ?

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

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prove 1+cot^2(θ)= 1/(sin^2(θ))

prove

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

True

Solution steps

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

Manipulating left side

1 + cot^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ^{2} ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

sin (2 π - x) = - sin (x)

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

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

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

sin^{2} (a) + sin^{2} (a) tan^{2} (a) = tan^{2} (a)

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