Question

I don't know how to get started on this sums and difference expression: sin θ - √︎3 cos θ =1

Answer 1

We are given:

Sinθ - √3 Cosθ = 1

Solving for θ:

dividing both the sides by 2

1/2 Sinθ - √3/2 Cosθ = 1/2

Cos(60°)*Sinθ - Sin(60°)Cosθ = Sin(30°) [Since Cos(60°) = 1/2 and Sin(60°)=√3/2]

We can see that the LHS resembles the formula:

Sin(A - B) = SinACosB - SinBCosA

Sin(θ - 60°) = Sin(30°)

So, we can say that:

θ - 60 = 30

θ = 90° or π/4 radians