Question

How would you solve cos(5x)=sin(10x) ?

Answer 1

Simplify using:\[\sin(10x)=2\sin(5x)\cos(5x)\]

Answer 2

how do you know that?

Answer 3

using the rule:\[\sin(2x)=\sin(x+x)=\sin(x)\cos(x)+\cos(x)\sin(x)=2\sin(x)\cos(x)\]

Answer 4

right, but how come you can separate the 10x to 5x?

Answer 5

\[\sin(10x)=\sin(5x+5x)=...\]

Answer 6

oh! i see, thank you!

Answer 7

yw

Answer 8

does that mean you do
\[\cos(5x)= 2\sin(5x)+2\cos(5x)\] ?

Answer 9

and then \[0= 2\sin(5x)-\cos(5x) ?\]

Answer 10

no, it should be:\[\cos(5x)=\sin(10x)=2\sin(5x)\cos(5x)\]
then cancel the \(\cos(5x)\) terms from left and right hand sides to leave:\[1=2\sin(5x)\]

Answer 11

oh dear, I don't know why I added an addition since in there. That makes more sense