Question

If cos(3x)=sin(x+18°) what is the value of x

Answer 1

Use the identity,

`\cos(90^\circ-x)=\sin x\implies \sin(x+18^\circ)=\cos(90^\circ-(x+18^\circ))=\cos(72^\circ-x)`

This lets us write

`\cos(3x)=\cos(72^\circ-x)`

and we can take the inverse cosine of both sides to get

`3x=72^\circ-x+360^\circ n\text{ OR }3x=x-72^\circ+360^\circ n`

where
`n` is any integer.

Solving for
`x` gives

`x=18^\circ+90^\circ n\text{ OR }x=-36^\circ+180^\circ n`