Is (1-sin(θ))(1+sin(θ))= 1/(sec^2(θ)) ?

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

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prove (1-sin(θ))(1+sin(θ))= 1/(sec^2(θ))

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{sec ^{2} ( θ )}

Express with sin, cos

= cos^{2} (θ)

Rewrite using trig identities

= (1 + sin (θ)) (1 - sin (θ))

= (1 - sin (θ)) (1 + sin (θ))

We showed that the two sides could take the same form

\Rightarrow True

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

sin^{2} (x) - 2 cos^{2} (x) = 1 - 3 cos^{2} (x)

\frac{1}{sin ^{2} ( x )} = csc^{2} (x)

\frac{sin ( x )}{1 + cos ( x )} + cot (x) = csc (x)

cos (θ - \frac{π}{2}) = sin (θ)

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