Hi,

 

Vibhu, your first step may be correct but solving ( 1 - t² )^9/2 would be a herculean task.

 

According to me, first step :  (cos²x)⁴

Second Step : ( 1 + cos2x )⁴ / 16 

Open it up.

Then, in the terms where 'cos' occurs in a power-2 or 4, convert it as i said in Step I.

And, then integrate it. It is a bit lengthy, but you will get the answer. And, this question does not come in entrance exams. And has a very less chance of being given in CBSE. But yes, you can do it to strengthen your concepts.