Integrate ::

sin(x-a)/sin(x+a)

sin(x-a)sin(x+a)dxWrite sin(x-a) as sin{(x+a)-2a}, and sin(A-B) = sinAcosB-cosAsinBSosin(x-a)sin(x+a)dx=sin(x+a)cos2a-cos(x+a)sin2asin(x+a)dxSo sin(x+a)cos2asin(x+a)dx-cos(x+a)sin2asin(x+a)dxOr cos2adx-tan(x+a)sin2adxAnd tanx=-log(cosx)+CHence cos2adx-tan(x+a)sin2adx=xcos2a +logcos(x+a)sin2a+C Hence sin(x-a)sin(x+a)dx=xcos2a +logcos(x+a)sin2a+C  (Ans)

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write sin(x-a) as sin[(x+a)-2a]......xpand it by sinA+B

fir niche wale sin(x+a) se upar kaekcut jayega or 2ra tan(x+a) banega

ANS: x.cos2a + sin2a.lncos(x+a) +k

orly kiya h to shayad galat ho sakta hai.....concept yahi hai......waise a=0 pe x ana chahiye jo ans me aa rha h to sahi hi hoga

posted by awan bhati (guiding students) AIR 134 IIT JEE 2013

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