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

The general solution for sin(x+60)=2cos(x) is x=1.15551…+180n

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

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

x = 1.15551 \dots + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Subtract

2 cos (x)

from both sides

\frac{1}{2} sin (x) + \frac{3 - 4}{2} cos (x) = 0

Simplify

\frac{1}{2} sin (x) + \frac{3 - 4}{2} cos (x) : \frac{sin ( x ) + ( 3 - 4 ) cos ( x )}{2}

\frac{sin ( x ) + ( 3 - 4 ) cos ( x )}{2} = 0

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

sin (x) + (3 - 4) cos (x) = 0

Rewrite using trig identities

tan (x) + 3 - 4 = 0

Move

3

to the right side

tan (x) - 4 = - 3

Move

4

to the right side

tan (x) = - 3 + 4

Apply trig inverse properties

x = arctan (- 3 + 4) + 18 0^{\circ} n

Show solutions in decimal form

x = 1.15551 \dots + 18 0^{\circ} n

sin (9 x) = sin (x)

cot^{3} (x) + 2 cot^{2} (x) - 3 cot (x) - 6 = 0

sin^{2} (x) = cos^{3} (x)

12 cot^{2} (x) - cot (x) = 1

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

What is the general solution for sin(x+60)=2cos(x) ?
The general solution for sin(x+60)=2cos(x) is x=1.15551…+180n