Question

If sin (A+B) = sinA cosB + cosA sinB & cos(A-B) = cosA cosB + sinA sinB, find the values of (1)
sin75° (2)cos15°.

Answer 1

Hi there.

1.] sin(A + B) = sin A.cos B + cos A.sin B.

→ sin 75° = sin (45 + 30)

= Sin 45 Cos 30 + Cos 45 Sin 30.

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

= [√3 + 1] / 2√2

2.] cos(A - B) = cos A.cos B + sin A.sin B.

→ cos 15° = cos (60 - 45)

= 1 + √3 / 2√2

Hope it helps! :)