Is sin(2θ)=(2cot(θ))/(1+cot^2(θ)) ?

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

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prove sin(2θ)=(2cot(θ))/(1+cot^2(θ))

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

= sin (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (A) csc (A) = cot (A)

tan (θ) = \frac{1 - cos ( 2 θ )}{sin ( 2 θ )}

cos^{2} (x) = sin^{2} (x) cos^{2} (x) + cos^{4} (x)

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

csc (2 θ) + cot (2 θ) = cot (θ)

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