Question

show that #Integrals

Answer 1

1+cos2x
= 1 + cos²x - sin²x
= 1 + 2cos²x - 1
= 2cos²x
so
√(1+cos2x)dx = cosx√2 dx

integrate it to get
√2 sinx + C

Answer 2

Hi friend,

The formulas for cos2x are

1. Cos2x = cos²x-sin²x......(1)
2.cos2x = 2cos²x-1.....(2)

Take 1+cos2x

= 1+ cos²x-sin²x(from 1)

= 1+2cos²x-1
= 2cos²x

Taking square root on both the sides,

= √2 cosx

By doing integration,

= √2 sinx +c.

Hope this helped you a little!!!