Solving trig equations using Addition formula

[studentxlol]

1. The problem statement, all variables and given/known data

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

2. Relevant equations

sinAcosB+cosAsinB

3. 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! :smile:

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]

1. The problem statement, all variables and given/known data

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

2. Relevant equations

sinAcosB+cosAsinB

3. 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.