InterviewSolution
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InterviewSolution
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`int(dx)/(cos x-sinx)` is equal toA. `(1)/(sqrt2)log|tan((x)/(2)-(pi)/(8))|+C`B. `(1)/(sqrt2)log|cot((x)/(2))|+C`C. `(1)/(sqrt2)log|tan((x)/(2)-(3pi)/(8))|+C`D. `(1)/(sqrt2)log|tan((x)/(2)+(3pi)/(8))|+C` |
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Answer» Correct Answer - D `l=int(dx)/(cosx-sinx)` `=(1)/(sqrt2)int(dx)/(((1)/(sqrt2)cosx-(1)/(sqrt2)sinx))` `=(1)/(sqrt2)int(dx)/(cos(x+(pi)/(4)))` `=(1)/(sqrt2)intsec(x+(pi)/(4))dx` `=(1)/(sqrt2)log|tan((pi)/(4)+(x)/(2)+(pi)/(8))|+C` `=(1)/(sqrt2)log|tan((x)/(2)+(3pi)/(8))|+C` |
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