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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{1 - sin ( β )} + \frac{1}{1 + sin ( β )}

Simplify

\frac{1}{1 + sin ( β )} + \frac{1}{1 - sin ( β )} : \frac{2}{( sin ( β ) + 1 ) ( - sin ( β ) + 1 )}

= \frac{2}{( 1 + sin ( β ) ) ( 1 - sin ( β ) )}

Rewrite using trig identities

= \frac{2}{cos ^{2} ( β )}

Rewrite using trig identities

2 sec^{2} (β)

We showed that the two sides could take the same form

\Rightarrow True

cos (x + \frac{3}{2} π) = sin (x)

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

\frac{csc ( θ ) sin ( θ )}{cot ( θ )} = tan (θ)

1 + tan^{2} (x) = cos^{2} (x) + sin^{2} (x)

cot^{2} (A) - cos^{2} (A) = cot^{2} (A) cos^{2} (A)

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