Question

Prove : sin theta + root 3 cos theta = 1

Answer 1

Answer:

The equation √3cosθ + sinθ = 1 is not valid for all values of θ (try θ = 0, for example)

To solve the equation, multiply and divide the left side by √ [(√3)2 + 12] = 2 to get:

2 [(√3 / 2)cosθ + (1/2)sinθ] = 1

2[cos30ºcosθ + sin30ºsinθ] = 1

2cos(θ - 30º) = 1

cos(θ - 30º) = 1/2

θ - 30º = 60º or 300º

θ = 90° or 330° (these are the solutions between 0° and 360°)

All solutions: 90° + k(360°) or 330° + k(360°), where k = 0, ±1, ±2, ...

hope it's helpful to you