What is the general solution for 2sin(x+60)=cos(x+30) ?

The general solution for 2sin(x+60)=cos(x+30) is x=150+180n

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2sin(x+60)=cos(x+30)

2 sin (x + 6 0^{\circ}) = cos (x + 3 0^{\circ})

x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

2 sin (x + 6 0^{\circ}) = cos (x + 3 0^{\circ})

Rewrite using trig identities

sin (x) + 3 cos (x) = \frac{3}{2} cos (x) - \frac{1}{2} sin (x)

Subtract

\frac{3}{2} cos (x) - \frac{1}{2} sin (x)

from both sides

\frac{3}{2} sin (x) - \frac{3}{2} cos (x) + 3 cos (x) = 0

Simplify

\frac{3}{2} sin (x) - \frac{3}{2} cos (x) + 3 cos (x) : \frac{3 sin ( x ) + 3 cos ( x )}{2}

\frac{3 sin ( x ) + 3 cos ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 sin (x) + 3 cos (x) = 0

Rewrite using trig identities

3 tan (x) + 3 = 0

Move

3

to the right side

3 tan (x) = - 3

Divide both sides by

3

tan (x) = - \frac{3}{3}

General solutions for

tan (x) = - \frac{3}{3}

x = 15 0^{\circ} + 18 0^{\circ} n

cot^{2} (θ) - 3 csc (θ) = - 3

tan^{3} (x) = \frac{1}{3} tan (x)

cos^{2} (x) = \frac{2}{3}

5 ∣ tan (x) ∣ = 5

3 arccos (x) = 2

What is the general solution for 2sin(x+60)=cos(x+30) ?
The general solution for 2sin(x+60)=cos(x+30) is x=150+180n