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`int_(pi//4)^(3pi//4)(dx)/(1+cosx)` is equal toA. 2B. `-2`C. `(1)/(2)`D. `-(1)/(2)` |
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Answer» Correct Answer - A Let `I=int_(pi//4)^(3pi//4)(dx)/(1+cosx)` . . . (i) `rArrI=int_(pi//4)^(3pi//4)(dx)/(1+cos(pi-x))` `I=int_(pi//4)^(3pi//4)(dx)/(1+cosx)` . . . (ii) On adding Eqs . (i) and (ii) , we get `2I=int_(pi//4)^(3pi//4)((1)/(1+cosx)+(1)/(1-cosx))`dx `rArr2I=int_(pi//4)^(3pi//4)((2)/(1-cos^(2)x))`dx `rArrI=int_(pi//4)^(3pi//4)"cosec"^(2)xdx=[-cotx]_(pi//4)^(3pi//4)` `=[-cot(3pi)/(4)+cot(pi)/(4)]=-(-1)+1=2` |
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