Answer :
Take L.H.S:
sin 65° + cos 65°
= sin 65° + sin (90° - 65°)
{sin (90° - A) = cos A}
= sin 65° + sin 25°
= 2 sin 45° cos 20°
= R.H.S
Hence Proved
ii. Take L.H.S:
sin 47° + cos 77°
= sin 47° + sin (90° - 77°)
{sin (90° - A) = cos A}
= sin 47° + sin 13°
= 2 sin 30° cos 17°
= cos 17°
= R.H.S
Hence Proved
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