Question

Please explain your answer. THX!!!!

Answer 1

Answer:

1)$cos(x)sin^{2}x$

2)0

Step-by-step 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

=$cos\frac{5\pi }{8}cos\frac{\pi }{8} + sin\frac{5\pi }{8}sin\frac{\pi }{8}$

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

=$cos(\frac{5\pi }{8} -\frac{\pi }{8})$

=$cos\frac{4\pi }{8}$

=$cos\frac{\pi }{2}$

=0!