Question

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation. sine of x divided by one minus cosine of x + sine of x divided by one plus cosine of x = 2 csc x

Answer 1

(sin(x)/(1-cosx))+sinx/(1+cosx)=2cscx

multiply both parts the left hand side by (1+cosx) and (1-cosx) respectively to get:

(sinx(1+cosx))+sinx(1-cosx))/(1-cos^2(x))

Simplify by the pythagorean identity, factoring and basic algebra:

(sin(x)(1+cosx+1-cosx))/(sin^2(x))

2/sin(x)=2cscx