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]