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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Expand

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

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

cos (x) (tan (x) - sec (- x)) = sin (x) - 1

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

sec^{2} (θ) - tan^{2} (θ) = 1

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

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

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