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

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