Is cos^2(x)(1-sec^2(x))=-sin^2(x) ?

The answer to whether cos^2(x)(1-sec^2(x))=-sin^2(x) is True

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prove cos^2(x)(1-sec^2(x))=-sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (x) (1 - sec^{2} (x))

Express with sin, cos

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

Rewrite using trig identities

= - sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (θ) - cos^{2} (θ) = 1

tan^{2} (θ) csc^{2} (θ) = sec^{2} (θ)

(tan (x) + cot (x))^{2} = sec^{4} (x) cot^{2} (x)

(1 + tan^{2} (s)) (1 - sin^{2} (s)) = 1

8 - 4 csc^{2} (z) = 4 - 4 cot^{2} (z)

Is cos^2(x)(1-sec^2(x))=-sin^2(x) ?
The answer to whether cos^2(x)(1-sec^2(x))=-sin^2(x) is True