sum ot difference!!!!!!!!!!!!!!!!

Question

Use Sum or difference identity to find SIN 15 degree

Answer 1

sin15° = sin(45° - 30°)                             [ We can write 15 as 45 - 30 ]                

= (sin45°*cos30°) - (cos 45°*sin30°)       [ Since sin(A - B) = sinAcosB - cosAsinB ]

= (1/√2)*(√3/2) - (1/√2)*(1/2)                   [ Since sin45°=cos 45°=1/√2 , cos30°=√3/2 and sin30°=1/2 ]

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

= (√6/4) - (√2/4)

= ¼(√6 - √2)

Therefore sin15° = ¼(√6 - √2)