Is (1-cos^2(θ))/(tan^2(θ))=cos^2(θ) ?

The answer to whether (1-cos^2(θ))/(tan^2(θ))=cos^2(θ) is True

Popular >

prove (1-cos^2(θ))/(tan^2(θ))=cos^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (θ) cos^{2} (θ) = sin^{2} (θ)

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

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

\frac{tan ( a )}{sec ( a )} = sin (a)

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

Is (1-cos^2(θ))/(tan^2(θ))=cos^2(θ) ?
The answer to whether (1-cos^2(θ))/(tan^2(θ))=cos^2(θ) is True