Is sec^2(θ)csc^2(θ)=sec^2(θ)+csc^2(θ) ?

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

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prove sec^2(θ)csc^2(θ)=sec^2(θ)+csc^2(θ)

prove

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

True

Solution steps

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

Manipulating right side

sec^{2} (θ) + csc^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

sec^{2} (θ) csc^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

tan (\frac{x}{2}) = \frac{sin ( x )}{1 + cos ( x )}

6 cos^{2} (x) - 6 sin^{2} (x) = 12 cos^{2} (x) - 6

sin (θ) cot (θ) sec (θ) = 1

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