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

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

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

prove

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

True

Solution steps

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

Manipulating right side

tan^{2} (y) sin^{2} (y)

Rewrite using trig identities

= tan^{2} (y) (1 - cos^{2} (y))

Expand

(1 - cos^{2} (y)) tan^{2} (y) : tan^{2} (y) - tan^{2} (y) cos^{2} (y)

= tan^{2} (y) - cos^{2} (y) tan^{2} (y)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) (1 + cot^{2} (θ)) = csc (θ)

csc (x) - sin (x) = csc (x) cot (x)

5 + cot^{2} (x) = 4 + csc^{2} (x)

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

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

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