Simplifying trig functions

Question

(5/1-sin(x))+(5/1+sin(x))

Answer 1

(5/1-sin(x))+(5/1+sin(x))

The common denominator will be (1-sin x)(1+sinx)

Multiply the first fraction top and bottom by (1+sinx) and multiply the second fraction top and bottom by (1-sinx)

(5(1+sinx) +5(1-sinx))/(1-sinx)(1+sinx)

Distribute top and bottom

(5 + 5sin x + 5 -5sinx)/1-sin²x

Combine like terms

The answer is

10/cos²x

Because the identity sin² x + cos²x=1

Subtracting sin² x from both sides yields

Cos²x=1-sin²x