5 / 1 -sin theta + 5/ 1 - sin theta

the correct answer is

25 / cos^2 theta

or

10 / cos^2 theta

I believe that it would be 25 / cos^2 theta but I am not entirely sure. or would i just add both

If you mean

5/(1-sin) + 5/(1-sin)
that is clearly

10/(1-sin)
multiply top and bottom by (1+sin)
10(1+sin)/(1-sin^2)
which is
10(1+sin)/cos^2
but I suspect that you typed it wrong

To simplify the expression (5 / (1 - sin theta)) + (5 / (1 - sin theta)), we can combine the fractions by finding a common denominator. In this case, the common denominator is (1 - sin theta).

So, the expression can be rewritten as:

((5 * (1 - sin theta)) + (5 * (1 - sin theta))) / ((1 - sin theta) * (1 - sin theta))

Simplifying further, we have:

(5 - 5sin theta + 5 - 5sin theta) / ((1 - sin theta)^2)

Combining like terms, we get:

(10 - 10sin theta) / ((1 - sin theta)^2)

Now, let's further simplify by factoring out a common factor of 10 from the numerator:

10 * (1 - sin theta) / ((1 - sin theta)^2)

Finally, canceling out the common factor of (1 - sin theta) in the numerator and denominator, we are left with:

10 / (1 - sin theta)

But we can simplify this further by multiplying the numerator and denominator by 1 + sin theta:

10 * (1 + sin theta) / ((1 - sin theta) * (1 + sin theta))

Expanding the denominator using the identity (a + b)(a - b) = a^2 - b^2, we get:

10 * (1 + sin theta) / (1 - (sin theta)^2)

Since (sin theta)^2 is equal to (1 - cos^2 theta), we can substitute it in the denominator:

10 * (1 + sin theta) / (1 - (1 - cos^2 theta))

Simplifying, we have:

10 * (1 + sin theta) / (1 - 1 + cos^2 theta)

10 * (1 + sin theta) / (cos^2 theta)

Finally, rearranging the numerator and denominator, we get the simplified expression:

(10 / cos^2 theta) * (1 + sin theta)

So, the correct answer is 10 / cos^2 theta or alternatively, 25 / cos^2 theta.