Evaluate the following integrals:
Expanding (cos x + sin x)2 = cos2x + sin2x + 2 sinx cosx
We know cos2x + sin2x = 1, 2sinxcosx = sin2x
∴ (cos x + sin x)2 = 1 + sin2x
∴ we can write the given equation as
⇒
Assume 1 + sin2x = t
⇒
⇒ 2cos2x dx = dt
∴ cos2xdx =
Substituting these values in the above equation we get
⇒
⇒ + c
substituting t = 1 + 2 sin x in above equation
⇒