Is sec^2(θ)=(sec^2(θ)-1)*csc^2(θ) ?

The answer to whether sec^2(θ)=(sec^2(θ)-1)*csc^2(θ) is True

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prove sec^2(θ)=(sec^2(θ)-1)*csc^2(θ)

prove

sec^{2} (θ) = (sec^{2} (θ) - 1) \cdot csc^{2} (θ)

True

Solution steps

sec^{2} (θ) = (sec^{2} (θ) - 1) csc^{2} (θ)

Manipulating right side

(sec^{2} (θ) - 1) csc^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ^{2} ( θ )}

Rewrite using trig identities

sec^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

csc (ω) - sin (ω) = cot (ω) cos (ω)

\frac{cot ( 3 θ ) - tan ( 3 θ )}{sin ( 3 θ ) + cos ( 3 θ )} = csc (3 θ) - sec (3 θ)

sin (- \frac{π}{2} - θ) = - cos (θ)

- 2 cos (2 x) \cdot sin (2 x) = sin (- 4 x)

Is sec^2(θ)=(sec^2(θ)-1)*csc^2(θ) ?
The answer to whether sec^2(θ)=(sec^2(θ)-1)*csc^2(θ) is True