Is 1/(sec^2(θ))+1/(csc^2(θ))=1 ?

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

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prove 1/(sec^2(θ))+1/(csc^2(θ))=1

prove

\frac{1}{sec ^{2} ( θ )} + \frac{1}{csc ^{2} ( θ )} = 1

True

Solution steps

\frac{1}{sec ^{2} ( θ )} + \frac{1}{csc ^{2} ( θ )} = 1

Manipulating left side

\frac{1}{sec ^{2} ( θ )} + \frac{1}{csc ^{2} ( θ )}

Express with sin, cos

= cos^{2} (θ) + sin^{2} (θ)

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

cos (x + π) cos (x - π) = cos^{2} (x)

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

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

sec^{3} (x) = \frac{1}{cos ^{3} ( x )}

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