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

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

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

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{sec ^{2} ( x )}

Express with sin, cos

= cos^{2} (x)

Rewrite using trig identities

= (1 + sin (x)) (1 - sin (x))

We showed that the two sides could take the same form

\Rightarrow True

sin (3 x) cos (2 x) - cos (3 x) sin (2 x) = sin (x)

4 cot^{2} (y) (sec^{2} (y) - 1) = 4

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

sin^{2} (x) sec (x) = \frac{sin ( x )}{cot ( x )}

cot^{2} (x) (1 + tan^{2} (x)) = csc^{2} (x)

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