Question

How do you write `3 sin pix + 3 (sqrt 3) cos pix` only in terms of sin?

Answer 1

`=6sin(pix+pi/3)`

Explanation:

`3 sin pix + 3 (sqrt 3) cos pix`
`=6 (1/2xxsin pix +(sqrt 3)/2 cos pix)` ( taking 6 common)
putting `1/2=cos(pi/3) and sqrt3/2=sin(pi/3)`

`=6 (cos(pi/3)xxsin pix+sin(pi/3) cos pix)`
applying formula `sinAcosB+cosA sinB=sin(A+B)`
`=6sin(pix+pi/3)`