Question

simplify


sin1140°cos390°-cos780°sin750°

need answer in full method ​

Answer 1

QUESTION:

simplify

simplifysin1140°cos390°-cos780°sin750°

ANSWER:

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° sin 30°

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

Answer:

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° = sin 60° cos30° - cos60° sin30°

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

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

hence the answer is 1/2.

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