Respuesta :

We can simplify the equation by taking the LCM, as shown below. 
Note: I have used x in place of Ф as equation editor does not contain the symbol Ф. The steps will be same, regardless of the variable.

[tex] \frac{1}{1+sin(x)} + \frac{1}{1-sin(x)} \\ \\ = \frac{1-sin(x)+1+sin(x)}{(1+sin(x))(1-sin(x))} \\ \\ = \frac{2}{1-sin^{2}(x) } \\ \\ = \frac{2}{cos^{2}(x) } \\ \\ =2sec^{2}(x) [/tex]

So, the answer to this questions is 2 sec²(Ф)
hisroyal1
[1/(1+ sinθ)] + [1/(1- sinθ)]

= [(1 - sinθ) + (1 + sinθ)] / [(1+ sinθ)(1- sinθ)]

= (1 - sinθ + 1 + sinθ) / (1 - sinθ + sinθ - sin²θ)

= (1 + 1 - sinθ + sinθ) / (1 - sin²θ)

= 2/(1-sin²θ)

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