Question

I need help with one of my questions from Pre-Calculus...

Answer 1

\[1+\cos10x=2\cos ^{2}5x\]

Answer 2

I am unsure as to how to start simplifying this. Help would be appreciated.

Answer 3

simplify?
do you mean the equation?

Answer 4

do you mean solve the equation?*

Answer 5

The textbook says to prove whether it is an identity. So solve it I guess

Answer 6

oh identities...

Answer 7

try using a double angle identity on cos(10x)

Answer 8

Which one should I use?

Answer 9

which identity?

Answer 10

the double angle identity for cosine

Answer 11

\[\cos(10x)=\cos(2 \cdot 5x)=...\]

Answer 12

Aren't there 3?
cos2x=cos^2x-sin^2x

Answer 13

you have your x there should be 5x

Answer 14

\[\cos(2 [5x])=\cos^2(5x)-\sin^2(5x)\]

Answer 15

now since the other side is written in terms of cosine write this in terms of cosine

Answer 16

you can use a Pythagorean identity

Answer 17

Ok, I think I can get it from here. Thanks for the explanation ^^

Answer 18

np