Question

How can
√3 cos a−sin a=2((√3/2) cos a− (1/2) sin a)
become
2(cos θ cos a - sin θ sin a)
and then become
2 cos (a + θ)


Can someone explain this please?

Answer 1

do you know how to expand out \(\cos(a+\theta)\)?

Answer 2

Ah that's where it comes from ok, sorry I didn't see that. But what happens to the \[\sqrt{3}/2 \] and the 1/2 ?

Answer 3

expand \(\cos(a+\theta)\) and then see which terms equate to \(\frac{\sqrt{3}}{2}\) and \(\frac{1}{2}\) - you should then be able to spot what to do next

Answer 4

i.e. you have:\[2(\frac{\sqrt{3}}{2}\cos(a)-\frac{1}{2}\sin(a))=2(\cos(\theta)\cos(a)-\sin(\theta)\sin(a))\]look at this identity and see what it tells you

Answer 5

ok... I think I've got it

Answer 6

great! :)

Answer 7

Thanks

Answer 8

yw :)