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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Expand

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

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

cos (x) - cos (x) sin^{2} (x) = cos^{3} (x)

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

cos (x + \frac{3 π}{2}) = sin (x)

1 - tan^{4} (A) = 2 sec^{2} (A) - sec^{4} (A)

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

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