Sin38°+sin22°=sin82
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Rohitkumar Gupta 7 years, 7 months ago
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°
2Thank You