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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Factor

tan^{2} (x) - sin^{2} (x) tan^{2} (x) : tan^{2} (x) (1 - sin^{2} (x))

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

Rewrite using trig identities

= cos^{2} (x) tan^{2} (x)

Express with sin, cos

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

csc (2 x) = \frac{csc ( x )}{2 cos ( x )}

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

cos (θ + \frac{π}{2}) = - sin (θ)

sin^{2} (a) + cos^{2} (a) = 1

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