Question

Please explain your answer. THX!!!!

Answer 1

1)
`cos(x)sin^(2)x`

2)0

Explanation:

for part 1:

Given cos(x) - cos^3(x)

= cos(x) (1- cos^2(x))

Using the identity
`cos^(2)x +sin^(2)x=1\\ sin^(2)x=1-cos^(2)x`

= cos(x)sin^2(x)

for part 2:

given

=
`cos(5\pi )/(8)cos(\pi )/(8)  + sin(5\pi )/(8)sin(\pi )/(8)`

Using the identity cos(a)cos(b) + sin(a)sin(b)= cos(a-b)

=
`cos((5\pi )/(8) -(\pi )/(8))`

=
`cos(4\pi )/(8)`

=
`cos(\pi )/(2)`

=0!