Question

I'm trying to find sin of (7pi/12) exactly using an angle of addition or subtraction formula could anyone help me​

Answer 1

(√2 + √6)/4.

Explanation:

Use the addition formula

sin (A+ B) = sinAcosB + cosAsinB

sin (7pi/12) = sin( 3pi/12 + 4pi/12)

= sin(pi/4 + pi/3) = sin pi/4 cos pi/3 + cos pi/4 sin pi/3

= 1/√2 * 1/2 + 1/√2 * √3/2 (using the 45-45-90 and 30-60-90 triangles)

= 1 / 2√2 + √3/2√2

= √2/4 + √6/4

= (√2 + √6)/4