Question

Use the Pythagorean identity to do the following:

b. Rewrite the expression (1 − cos2(theta)) csc(theta) in terms of a single trigonometric function. State the resulting
identity

Answer 1

Answer: 2sin(θ)

Step-by-step explanation: (1 − cos2(theta)) csc(theta)

cos (2θ) = cos²(θ) - sin²(θ) ⇒ [(1 - cos²(θ) + sin²(θ)]* csc (θ)

Multiplying csc(θ) - cos²(θ)*csc(θ) + sin²(θ)*csc(θ)

csc (θ) = 1 ÷ sin (θ) ⇒ 1/sin(θ) - cos²(θ)/sin(θ) + sin²(θ)/sin(θ)

1/sin(θ) [ 1 -cos²(θ) + sin²(θ)] ⇒ 1- cos²(θ) = sin²θ)

1/sin(θ) [ sin²(θ) +sin²(θ) ]

1/sin(θ) [ 2* sin²(θ) ] = 2sin(θ)