InterviewSolution
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InterviewSolution
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`int(cos 2x)/((sin x + cos x)^(2)) dx " is equal to : "`A. `log|sin x+cos x|+C`B. `log|sin x-cos x|+C`C. `(1)/((sin x+ cos x)^(2))`D. |
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Answer» Correct Answer - b `" Let I "= int(cos2x)/((sin x + cos x)^(2))dx` `=int(cos^(2) x-sin^(2)x)/((sin x+cos x)^(2))dx` ` =int((cos x-sin x)(cos x+ sin x))/((sin x+cos x)(sin x+cos x))dx` `=int( cos x- sinx)/(sin x+cos x)dx` `" Let " sin x cos x=t rArr (cos x-sin x) dx=dt` `:. I= int (1)/(t) dt= log|t|+C` `=log |sin x+cos x| +C` |
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