Question

cos2x-2sin^2x=0

Answer 1

\[\cos(2x)=\cos^2(x)-\sin^2(x) \text{ by double angle identity for cosine } \\ \cos(2x)=(1-\sin^2(x))-\sin^2(x) \text{ by Pythagorean Identity } \\ \cos(2x)=1-2 \sin^2(x) \text{ by collecting like terms }\]

Answer 2

so use cos(2x)=1-2sin^2(x)
to write the equation in terms of sin(x)

Answer 3

i got 2sin^2x+cos^2x-1=0

Answer 4

where do i go from here

Answer 5

why not use the identity I mentioned above

Answer 6

your equation becomes
\[1-2\sin^2(x)-2\sin^2(x)=0\]

Answer 7

ohh okay so i just solve that equation

Answer 8

yep
first isolate the sin^2(x) part

Answer 9

im not sure how to do that with the 1

Answer 10

i tried taking out the 2sin^2x

Answer 11

do you know how to add -2sin^2(x) and -2sin^2(x)?

Answer 12

and subtract 1 on both sides?