Question

Prove that root3 sin 10 degree + root2 sin 55 degree = cos 80 degree + 2 cos 50 degree

Answer 1

Answer:

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Step-by-step explanation:

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we have to prove that:

sin40°-cos70°=√3cos80° solution:-formula used;sin (90° - x ) = cos x&cos C - cos D = 2 sin { ( C+ D) /2 } sin { D -C ) /2} Here,Taking LHS ;sin40°-cos70° = sin (90° - 50° ) - cos 70° = cos 50° - cos 70° => 2 sin { (50°+70°)/2 } sin {(70°-50°)/2} => 2 sin 60° sin 10° => 2×√3/2 × sin 10° .(sin 60°=√3/2)=> √3 × sin (90° -80°)=> √3 cos 80° = RHS Hence;Proved ......

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