Help Verify this equation.

Question

1/1-cos(theta)+1/1+cos(theta)=2csc^2(theta)

Answer 1

First, combine the fractions on the left side using a common denominator (Hint: it will involve the products of the current denominators).

 

Next, recognize that this common denominator can be written as the difference of perfect squares (i.e. (x-a)*(x+a) = x^2-a^2)

 

Last, use the trig identities sin^2(th) = 1 -cos^2(th) and csc(th)=1/sin(th)

 

Good luck.

 

Paul

Answer 2

1 / (1 - cosθ) + 1 / (1 + cosθ) = 2 csc² θ

(1 + cosθ + 1 - cosθ) / [ (1 - cosθ)(1 + cosθ)] = 2 csc² θ

2 / (1 - cos² θ) = 2 csc²θ

2 / sin²θ = 2 csc² θ

2 csc² θ = 2 csc² θ