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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

= cos^{2} (a)

Rewrite using trig identities

= (1 + sin (a)) (1 - sin (a))

We showed that the two sides could take the same form

\Rightarrow True

sec (a) (1 - sin^{2} (a)) = cos (a)

cos (x + y) - cos (x - y) = - 2 sin (x) sin (y)

sec (\frac{π}{2} - u) = csc (u)

\frac{cot ^{3} ( t )}{csc ( t )} = cos (t) (csc^{2} (- 1))

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

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