Solving trig equations using Addition formula

[studentxlol]

Homework Statement

Solve the equation: sin(x+∏/6)=2cosx for 0≤x≤2∏

Homework Equations

sinAcosB+cosAsinB

The Attempt at a Solution

sin(x+∏/6)=2cosx

2cosx=(√3)/2sinx+1/2cosx

How do I solve from here?

 

[micromass]

Moved the thread to precalc. Please post in the correct forum next time.

 

[I like Serena]

Hi studentxlol!

Perhaps you can use the following trig identity?

a sin x + b cos x = √(a²+b²) sin(x+ϕ)

where cos ϕ = a/√(a²+b²)
and sin ϕ= b/√(a²+b²)

 

[HallsofIvy]

Homework Statement

Solve the equation: sin(x+∏/6)=2cosx for 0≤x≤2∏

Homework Equations

sinAcosB+cosAsinB

The Attempt at a Solution

sin(x+∏/6)=2cosx

2cosx=(√3)/2sinx+1/2cosx

How do I solve from here?

The first, obvious, step is to subtract (1/2) cos(x) from both sides. Then get a tangent.