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.)