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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