Q.

The value of ∫1/etan⁡x t1+t2dt+∫1/ecot⁡x dtt1+t2 is

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a

1/2

b

1

c

π/4

d

none of these

answer is B.

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Detailed Solution

1t1+t2=1t−t1+t2So the required integral is  equal to∫1etan⁡x tdx1+t2+∫1ecot⁡x dtt−∫1ecot⁡x tdt1+t2=12log⁡1+t21etan⁡x+log⁡t1ecot⁡x−12log⁡1+t21ecot⁡x=log⁡|sec⁡x|+log⁡|cot⁡x|+1−log⁡|cosec⁡x|=1
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