What is 1/(1-sin(θ))+1/(1+sin(θ)) ?

The solution to 1/(1-sin(θ))+1/(1+sin(θ)) is 2sec^2(θ)

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simplify 1/(1-sin(θ))+1/(1+sin(θ))

simplify

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

2 sec^{2} (θ)

Solution steps

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

Join

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

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

Simplify

(- sin (θ) + 1) (sin (θ) + 1) : cos^{2} (θ)

= \frac{2}{cos ^{2} ( θ )}

Use the basic trigonometric identity:

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

= 2 sec^{2} (θ)

\frac{2}{3} \div \frac{2}{3}

2 (3 + 4 y + 5)

1.5 \times 1.5

\frac{- 2}{2}

30000

What is 1/(1-sin(θ))+1/(1+sin(θ)) ?
The solution to 1/(1-sin(θ))+1/(1+sin(θ)) is 2sec^2(θ)