Is 1+sec^2(θ)sin^2(θ)=sec^2(θ) ?

The answer to whether 1+sec^2(θ)sin^2(θ)=sec^2(θ) is True

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prove 1+sec^2(θ)sin^2(θ)=sec^2(θ)

prove

1 + sec^{2} (θ) sin^{2} (θ) = sec^{2} (θ)

True

Solution steps

1 + sec^{2} (θ) sin^{2} (θ) = sec^{2} (θ)

Manipulating left side

1 + sec^{2} (θ) sin^{2} (θ)

Express with sin, cos

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

3 sin^{2} (x) + 4 cos^{2} (x) = 3 + cos^{2} (x)

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

sec (θ) + tan (θ) = \frac{cos ( θ )}{1 - sin ( θ )}

sin^{2} (x) - 3 cos^{2} (x) = 4 sin^{2} (x) - 3

tan^{2} (x) + 6 = sec^{2} (x) + 5

Is 1+sec^2(θ)sin^2(θ)=sec^2(θ) ?
The answer to whether 1+sec^2(θ)sin^2(θ)=sec^2(θ) is True