Question

To solve the equation 2sin(2x) = cosx, you should rewrite it as.......?
A. cosx(4sinx - 1) = 0
B. 2sinx + cosx = 0
C. cosx(2sinx - 1) = 0

Answer 1

I am sure you have seen this before,
\(\large\color{black}{ \displaystyle \sin(\color{red}{\rm a}+\color{blue}{\rm b})=\sin(\color{red}{\rm a})\cos(\color{blue}{\rm b})+\sin(\color{blue}{\rm b})\cos(\color{red}{\rm a}) }\)

what if your 'a' and 'b' are same?
(such that x+x) ?

Answer 2

sin2x = 2SinxCosx

re write it to get

2(2sinxcosx)=cosx
4sinxcosx-cosx=0
cosx(4sinx - 1)=0

Answer 3

\(\large\color{black}{ \displaystyle \sin(\color{red}{\rm x }+\color{blue}{\rm x})=\sin(\color{red}{\rm x})\cos(\color{blue}{\rm x})+\sin(\color{blue}{\rm x})\cos(\color{red}{\rm x})~~~~=\color{green}{2} \sin(\color{blue}{\rm x})\cos(\color{red}{\rm x})}\)

Answer 4

is this making sense?

Answer 5

\(\large\color{black}{ \displaystyle 2\sin(2\color{red}{\rm x }) = \cos(\color{red}{\rm x })}\)
re-writing
\(\large\color{black}{ \displaystyle \color{green}{2} \sin(\color{blue}{\rm x})\cos(\color{red}{\rm x})=\cos(\color{red}{\rm x })}\)

then subtract \(\large\color{black}{ \displaystyle \cos(\color{red}{\rm x })}\) from both sides, and factor on the left hand side to get the answer.

Answer 6

Awesome, thanks Solomon! My classes are all online so sometimes it's harder to remember whether we've gone over something or not.

Answer 7

@SolomonZelman

Answer 8

yes?