sin x cos x65.find |dxsinx cosx[2017 O.D set-11 1 mAns log sin 21+C

1.	sin x cos x65.find \|dxsinx cosx[2017 O.D set-11 1 mAns log sin 21+C
Answer» (Sinx -cosx)^2 = sin^2x + cos^2x -2sinx.cosx =1-2sinx.cosx =1-sin2x Sin^2x -cos^2x =-cos2x Integration -cos2x/(1-sin2x) 1-sin2x = t -2cos2x dx =dt Integration (-cos2x /t ) × dt/-2cos2x Integration 1/2 (1/t dt) =1/2 log\|t\| + log c log (1-sin2x )^1/2+logc log [(1-sin^2x)^1/2 ×c]

Answer»

(Sinx -cosx)^2 = sin^2x + cos^2x -2sinx.cosx =1-2sinx.cosx =1-sin2x

Sin^2x -cos^2x =-cos2x

Integration -cos2x/(1-sin2x)

1-sin2x = t

-2cos2x dx =dt

Integration (-cos2x /t ) × dt/-2cos2x

Integration 1/2 (1/t dt) =1/2 log|t| + log c

log (1-sin2x )^1/2+logc

log [(1-sin^2x)^1/2 ×c]

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