Trigonometry Question

Question

Prove sinx/1+cosx + 1+cosx/sinx = 2 cscx, Justify significant steps. Help!?

Answer 1

Find a common denominator:

sinx/(1+cosx)+(1+cosx)/sinx 

=(sinx)²+(1+cosx)²/(sinx(1+cosx))

=(sin²x+1+2cosx+cos²x)/(sinx(1+cosx))

 

Use an identity involving sin²x and cos²x, then simplify.