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)

- 7 \cdot 5

\frac{3}{2} + \frac{6}{4} + \frac{5}{8}

x^{2} + x - 30 \cdot \frac{x}{x ^{2} + 6 x}

(x + 1) (x^{2} + x + 1) (x - 1) (x^{2} - x + 1) + 1

\frac{1 5 ^{2} \cdot 25 \cdot 49}{3 5 ^{2} \cdot 4 5 ^{2}}

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)