Question

Sin 780° sin 480°+cos 120° costo60=1/2
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Answer 1

Answer:

To prove : Sin 780° sin 480°+cos 120° cos60°=1/2

LHS = sin 780° sin 480°+cos 120° cos60°

= sin(720+60)° . sin(450+30)° + cos(90+30)° cos60°

= sin60°. (cos30°) + (-sin30°).cos60°

= sin60°. cos30° - cos60°. sin30°

= sin(60-30)°          (using formula, sin(A-B) = sinA.cosB - cosA.sinB )

= sin30°

= 1/2

= RHS

=> LHS = RHS

Hence proved