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Sin38°+sin22°=sin82 |
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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) = sinФnow using here,we get,cos8° = cos(90 - 82)°⇒sin82°hence,sin38° + sin22° = sin82° Lhs sin38+sin22=2sin(38+22)/2. cos(38-22)/2=2sin30cos8=cos8=cos(90-8)=sin82 |
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