Question

Show that the equation sin(x-60) - cos(30-x) = 1 can be written in the form cosx = k, where k is a constant.

Answer 1

Please use these identities:
\[\begin{gathered}
\sin \left( {x - 60} \right) = \sin x\cos 60 - \cos x\sin 60 = \frac{1}{2}\left( {\sin x - \sqrt 3 \cos x} \right) \hfill \\
\cos \left( {30 - x} \right) = \cos 30\cos x + \sin 30\sin x = \frac{1}{2}\left( {\sqrt 3 \cos x + \sin x} \right) \hfill \\
\end{gathered} \]

Answer 2

Did alrd, i couldnt continue.

Answer 3

i got -sqrt3cos

Answer 4

that's right!
the left side is :
\[ - \sqrt 3 \cos x\]

Answer 5

then?

Answer 6

it's okay.

Answer 7

then you can write:
\[\begin{gathered}
- \sqrt 3 \cos x = 1 \hfill \\
\cos x = - \frac{1}{{\sqrt 3 }} \hfill \\
\end{gathered} \]

Answer 8

ok