Question -
Answer -
(i) sin 65o + cos 65o = √2cos 20o
Let us consider LHS:
sin 65o + cos 65o =sin 65o + sin (90o – 65o)
= sin 65o + sin 25o
By using the formula,
sin A + sin B = 2 sin (A+B)/2 cos (A-B)/2
sin 65o + sin 25o = 2sin (65o + 25o)/2 cos (65o – 25o)/2
= 2 sin 90o/2 cos 40o/2
= 2 sin 45o cos 20o
= 2 × 1/√2 × cos 20o
= √2 cos 20o
= RHS
Hence proved.
(ii) sin 47o + cos 77o =cos 17o
Let us consider LHS:
sin 47o + cos 77o =sin 47o + sin (90o – 77o)
= sin 47o + sin 13o
By using the formula,
sin A + sin B = 2 sin (A+B)/2 cos (A-B)/2
sin 47o + sin 13o = 2sin (47o + 13o)/2 cos (47o – 13o)/2
= 2 sin 60o/2 cos 34o/2
= 2 sin 30o cos 17o
= 2 × 1/2 × cos 17o
= cos 17o
= RHS
Hence proved.