Question

Simplify sin 1140° cos 390° - cos 780° sin 750°

Answer 1

we know,
sin(n × 360° + x) = sinx

cos(n × 360° + x) = cosx

sin1140° = sin(3 × 360° + 60°) = sin60°

cos390° = cos(1 × 360° + 30°) = cos30°

cos780° = cos(2 × 360° + 60°) = cos60°

sin750° = cos(2 × 360° + 30°) = sin30°

now, sin 1140° cos 390° - cos 780° sin 750° = sin60° cos30° - cos60° sin30°

use formula, sinA.cosB - cosA.sinB = sin(A - B)

so, sin60° cos30° - cos60° sin30° = sin(60° - 30°) = sin30° = 1/2

hence answer is 1/2

Answer 2

HELLO DEAR,



we know,
sin(n360° + x) = sinx

cos(n360° + x) = cosx

sin1140° = sin(3 × 360° + 60°) = sin60°

cos390° = cos(1 × 360° + 30°) = cos30°

cos780° = cos(2 × 360° + 60°) = cos60°

sin750° = cos(2 × 360° + 30°) = sin30°

now,
sin 1140° cos 390° - cos 780° sin 750° = sin60° cos30° - cos60° sin30°

[as, sinA.cosB - cosA.sinB = sin(A - B) ]

so, sin60° cos30° - cos60° sin30° = sin(60° - 30°) = sin30° = 1/2



I HOPE IT'S HELP YOU DEAR,
THANKS