Q. 1023.8( 8 Votes )

# Evaluate the following integrals:

Answer :

To find: Value of

Formula used:

We have, … (i)

Let (sinx – cosx) = t

t2 = sin2x - 2sinx. cosx + cos2x

t2 = 1 - 2sinx.cosx

2sinx.cosx = 1 - t2

sin2x = 1 - t2

Putting this value in equation (i)

Let

… (ii)

Now if

Then cosθ =

cosθ =

cosθ =

cosθ =

Now tanθ =

Now tanθ =

Comparing the value θ from eqn. (ii)

Dividing Numerator and denominator from cosx

Ans.)

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