Question

please evaluate help this to solve​

Answer 1

Answer:

This question is of trignometric integration.

First of all , we have to reduce it in the form of half angle of tan from cosine angle.

The formula used is

$\cos(2 \alpha ) = \frac{1 - { \tan }^{2} \alpha }{1 + { \tan}^{2} \alpha }$

Then we get the integral part in the form of secant angle in Numerator.

There, we have converted it into tan angle .

Formula used is,

$1 + { \tan }^{2} \alpha = { \sec}^{2} \alpha$

Further, reducing and converting into integrals we get,

an integral in form of,

$\frac{dx}{ {a}^{2} + {x}^{2} }$

And, we know that, its integration is ,

$\frac{1}{a} arc \tan( \frac{x}{a} )$

Here, arc means inverse.

And Hence we got the answer.

$\bold\red{Note:- Refer\:to\:the\:attachment.}$