Respuesta :

Given expression is [tex] \frac{1}{1+ sin \theta} + \frac{1}{1 - sin \theta} [/tex]

Now we can combine it as
[tex] \frac{1 - sin \theta + 1 + sin \theta}{(1+sin \theta)(1 - sin \theta)} [/tex]

Now we can use identity as [tex](a+b)(a-b) = a^2 - b^2[/tex]

[tex] \frac{2}{1 - sin^2 \theta} [/tex]

Now we can use identity as [tex]1 - sin^2 \theta = cos^2 \theta[/tex]

[tex] \frac{2}{1 - sin^2 \theta} = \frac{2}{cos^2 \theta} [/tex]

As we know [tex] \frac{1}{cos \theta} = sec \theta [/tex]

So [tex] \frac{2}{cos^2 \theta} = 2 sec^2 \theta [/tex]

So given expression equal to [tex]2sec^2 \theta[/tex]

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