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

Popular >

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 (θ) sec (\frac{π}{2} - θ) = cot (θ)

csc (x) (1 + sin (x)) = 1 + csc (x)

sin (x + y) sin (x - y) = sin (2 x) - sin (2 y)

csc^{2} (x) = 1 - cot^{2} (x)

cos^{2} (θ) = 1 + sin^{2} (θ)

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