Question

Use the double angle formula to solve: 10cos^2 x - 5
I have the formulas with me but I have no idea how to start this off

Answer 1

is it
\[10\cos^2(x) -5\]
?

Answer 2

yes

Answer 3

is that equal to zero?

Answer 4

no, that's all the problem says, that's why I'm having trouble

Answer 5

Then its an expression.
\[\cos(2a) = \cos^2(a)-\sin^2(a)\]
so \[\cos^2(a) = \cos(2a)+\sin^2(a)\]?
the issue is that you can't solve for something without an equation and an equals sign.

Answer 6

okay so how do I start this problem?

Answer 7

1) be very clear on what the problem asks you to do. What does it ask?
maybe it is \[10\cos^2(x) = 5\]?

Answer 8

It says, use the double angle formula to rewrite 10cos^2 x - 5

Answer 9

Skip it and move on unless its your last problem.
if it was
\[10\cos^2(x) =5\] then \[\cos^2(x) = 0.5\] and \[\cos(x) = \pm 0.25\]

Answer 10

i think u can slove it like
use multiple angle formula
cos(2x)=2cos^2(x)-1
so in ur case
10cos^2(x)=5
=> 5*(2cos^2(x))=5
=> 5*(1+cos(2x))=5
=> 1+cos(2x)=1 (dividing both side by 5)
=> cos(2x)=0

now solve for x