Is tan^2(x)=sin^2(x)+sin^2(x)tan^2(x) ?

The answer to whether tan^2(x)=sin^2(x)+sin^2(x)tan^2(x) is True

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prove tan^2(x)=sin^2(x)+sin^2(x)tan^2(x)

prove

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

True

Solution steps

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

Manipulating right side

sin^{2} (x) + sin^{2} (x) tan^{2} (x)

Rewrite using trig identities

= sin^{2} (x) sec^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

- sin (x) sec (x) = - tan (x)

cos (4 x) - cos (3 x) cos (x) = sin (2 x) - 4 cos (2 x) sin (2 x)

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

cos (4 x) = 1 - 8 sin^{2} (x) cos (x)

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

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