Is tan^2(θ)csc^2(θ)=1+tan^2(θ) ?

The answer to whether tan^2(θ)csc^2(θ)=1+tan^2(θ) is True

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prove tan^2(θ)csc^2(θ)=1+tan^2(θ)

prove

tan^{2} (θ) csc^{2} (θ) = 1 + tan^{2} (θ)

True

Solution steps

tan^{2} (θ) csc^{2} (θ) = 1 + tan^{2} (θ)

Manipulating left side

tan^{2} (θ) csc^{2} (θ)

Express with sin, cos

= \frac{1}{cos ^{2} ( θ )}

Manipulating right side

1 + tan^{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 )}

We showed that the two sides could take the same form

\Rightarrow True

cos (4 a) = 8 cos^{4} (a) - 8 cos^{2} (a) + 1

2 cos^{2} (x) + cos (x) = 0

csc^{2} (x) sec^{2} (x) = csc^{2} (x) + sec^{2} (x)

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

sin^{5} (x) = (1 - 2 cos^{2} (x) + cos^{4} (x)) (sin (x))

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