Question

Question #d27e0

Answer 1

See below.

Explanation:

Given

`sinx = x - x^3/(3!) + x^5/(5!) - x^7/(7!) + x^9/(9!) +cdots`

then

`sin x + x = 2x - x^3/(3!) + x^5/(5!) - x^7/(7!) + x^9/(9!) +cdots`

`sin x^2 = x^2 - x^6/(3!) + x^10/(5!) - x^14/(7!) + x^18/(9!) +cdots`

`cos x = d/(dx) sin x =1 - 3x^2/(3!) + 5x^4/(5!) - 7x^6/(7!) + 9x^8/(9!) +cdots`

`=1 - x^2/(2!) + x^4/(4!) - x^6/(6!) + x^8/(8!) +cdots`