Question

How do you solve the problem: 2cos^2x=sin2x

Answer 1

\[2\cos ^{2}x=\sin 2x\]Hint: Find the common identity for sin 2x.

Answer 2

So you get 2cos^2x = 2sinxcosx then what from there? Because I got that far.

Answer 3

sin 2x= 2sin x cos x
so
2 sin x cos x = 2 cos ² x
divide both sides by 2 cos ² x
(sin x)/(cos x)=1
tan x=1
x=arctan 1

Answer 4

How have you (Friesa) previously found angles in situations like this one: tan x = 1 or \[\tan x=\frac{ 1 }{ 1 }?\]

Answer 5

Note that while it is valid to divide both sides of the equation above by \[2 \cos ² x\] you must also set \[2 \cos ² x = 0\] and solve that for x also.

Answer 6

Please share your work here. Ask all the questions you want.