Question

If 3 cos θ= 2 sin θ then the value of 4 sin θ-3 cos θ/2 sin θ+6 cos θ

Answer 1

3cosθ = 2 sinθ
⇒sinθ/cosθ =3/2
⇒tanθ =3/2

Now, (4sinθ- 3 cosθ)/(2sinθ+6cosθ)
dividing num and deno by cosθ

=(4tanθ - 3)/(2tanθ +6)
=[4×(3/2)-3]/[2×(3/2)+6]
=(6-3)/(3+6)
=3/9
=1/3