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

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

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

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

x = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Subtract

2 cos (x)

from both sides

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

Simplify

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

General solutions for

tan (x) = 3

x = 6 0^{\circ} + 18 0^{\circ} n

(3 cos (x) + 2 sin (x))^{2} + 5 sin^{2} (x) = 9 - 33

7 cos (2 x) = 7 sin^{2} (x) + 5

2 cos^{2} (x) - sin (x) = - 1

\frac{cos ( x ) \cdot cot ( x )}{1 - sin ( x )} = 3

\frac{sin ( 8 )}{30} = \frac{sin ( θ )}{120}

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