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 left 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

tan (\frac{x}{2}) + cot (\frac{x}{2}) = 2 csc (x)

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

sin (\frac{3 π}{2} + x) = - cos (x)

\frac{cos ^{2} ( t )}{sin ( t )} = csc (t) - sin (t)

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

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