Evaluate the following integrals:

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.)