Answer:
1)[tex]cos(x)sin^{2}x[/tex]
2)0
Step-by-step explanation:
for part 1:
Given cos(x) - cos^3(x)
= cos(x) (1- cos^2(x))
Using the identity [tex]cos^{2}x +sin^{2}x=1\\ sin^{2}x=1-cos^{2}x[/tex]
= cos(x)sin^2(x)
for part 2:
given
=[tex]cos\frac{5\pi }{8}cos\frac{\pi }{8} + sin\frac{5\pi }{8}sin\frac{\pi }{8}[/tex]
Using the identity cos(a)cos(b) + sin(a)sin(b)= cos(a-b)
=[tex]cos(\frac{5\pi }{8} -\frac{\pi }{8})[/tex]
=[tex]cos\frac{4\pi }{8}[/tex]
=[tex]cos\frac{\pi }{2}[/tex]
=0!
