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Sin38°+sin22°=sin82°

Answer»

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


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