Question

prove sin 38 + sin 22 = sin 82

Answer 1

HELLO DEAR,


sin38° + sin22° = sin82°


Now,


from , L.H.S,

sin38° + sin22° = 2sin(38 + 22)/2 * cos(38 - 22)/2
∴ [ sinA + sinB = 2sin(A + B)/2 * cos(A - B)/2 ]


⇒2sin(60/2) * cos(16/2)


⇒2sin30° * cos8°


⇒2 * 1/2 * cos8°
∴ [ sin30° = 1/2 ]

⇒ 2̶ * 1/ 2̶ * cos8°


⇒cos8°



we know that:-

cos(90 - Ф) = sinФ


now using here,


we get,

cos8° = cos(90 - 82)°

⇒sin82°


hence,


sin38° + sin22° = sin82°



I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

HEY!!

___________________________

✴Consider LHS:

✔sin 38° + sin 22°

✔2sin (38° + 22°/2) cos (38° − 22°/2)

✔{∵ sin A + sin B = 2sin (A + B/2) cos (A − B/2)}

✔2sin 30° cos 8°= 2×1/2cos(90°-8°)

✔sin 82°= RHS

▶▶Hence, LHS=RHS.