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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

sin^{2} (θ) tan^{2} (θ)

Rewrite using trig identities

= (1 - cos^{2} (θ)) tan^{2} (θ)

Expand

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

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

Rewrite using trig identities

= tan^{2} (θ) - sin^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

(csc (x) + cot (x)) (csc (x) - cot (x)) = 1

cot^{2} (θ) - csc^{2} (θ) = - 1

\frac{sec ^{2} ( t ) - 1}{sec ^{2} ( t )} = sin^{2} (t)

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