Determine the solutions for:

Question

(cos x)/(1 + sinx) + (1 + sinx)/(cosx) = 2

in the interval x is all real numbers, such that [-2 pi, 2pi]

Answer 1

Multiply each term by cosx(1+sinx)

cos^2(x) + 1 + 2sinx + sin^2(x) = 2cosx(1+sinx)
2 + 2sinx = 2cosx(1+sinx) , recall sin^2(x) + cos^2(x) = 1

2(1 + sinx) = 2cosx(1+sinx)

now divide by 1+sinx to get

1 = cosx

for the given domain, x = -2pi,0,2pi