Question

Find the exact value of sin 165° by using a sum or difference formula

Answer 1

Answer: (√2 - √6)/4

Step-by-step explanation:

I am going to use the sum formula: sin(A + B) = sin A cos B  +  cos A sin B

Let's say A = 135° and B = 30°

sin(135° + 30°) = sin(135°) * cos(30°) + cos (135°) * sin(30°)

                       = (√2)/2 * 1/2 + (-√2)/2 * (√3)/2

                       = (√2)/4 + (-√6)/4

                       = (√2 - √6)/4