Prove that sin 16 degree + cos 16 degree  = 1/root 2 ( 3cos 1 degree+sin 1 degree )

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Guhiy
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L.H.S =sin16°+cos16° =sin16°+sin74° [ cosA=sin[90°- A] =2sin {(16°+74°)/2}×cos{(16°-74°)/2} =2sin45°cos29° =1/√2{2cos29°} =1/√2{2cos(30°-1°)} =1√2{2(cos30°cos1°+sin30°sin1°)} Applying the formula of cos(A+B) =1/√2[2{1/2 cos 1° + √3/2sin1°}] Opening the second brackets and cancelling out the twos we get; 1/√2(cos1°+√3sin1°) = R.H.S [ PROVED]
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Hots - 2

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