Simplify the expression

Question

asked Sep 2, 2023 126k views

1 Answer

Lawnsea · Answer 1 · 2023-09-07T14:27:36+0000

Answer:

(2)/(cos(x))

Explanation:

Key facts you will need to know to solve this

tan(x) = (sin(x))/(cos(x))

sin^2 + cos^2 = 1 so
1-sin^2= cos^2

The equation can also simplify by cross multiplying the fraction to make:

(cosx-sincosx)/((1+sinx)(1-sinx)) + (cosx+sincosx)/((1-sinx)(1+sinx))

(cosx-sincosx)/(1-sin^2(x)) + (cosx+sincosx)/(1-sin^2(x)) =
(2cos(x))/(1-sin^2(x))

Using the equation
1-sin^2= cos^2 that we established earlier, the fraction is also:

(2cos(x))/(cos^2(x)) =
(2)/(cos(x))

Therefore, the answer is
(2)/(cos(x))