Question

find sin 74 using sin a + b is equal to sin a cos b + cos a sin b​

Answer 1

Sin 75°= Sin (30° + 45°)

= Sin 30° Cos 45° + Sin 45° Cos 30°

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

= (1 / 2√2) + (√ 3 / 2 √2)

= (1 + √3) / 2 √2

On rationalising :-

(1 + √3) (2 √2) / (2√2) (2√2)

(2 √2 + 2 √6) / 8

2 (√2 + √6) / 8

(√2 + √6) / 4

Therefore Sin75°= (√2 + √6) / 4