What is 1/(1+sin(x))+1/(1-sin(x)) ?

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

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simplify 1/(1+sin(x))+1/(1-sin(x))

simplify

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

2 sec^{2} (x)

Solution steps

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

Join

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

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

Simplify

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

= \frac{2}{cos ^{2} ( x )}

Use the basic trigonometric identity:

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

= 2 sec^{2} (x)

(y + 2)^{3}

(1 + 2 x)^{2}

- 2 x - x

\frac{cos ( x )}{1 + sin ( x )} + tan (x)

2 (x + 5)

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