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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Subtract

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

from both sides

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

Simplify

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

1 = 2 cos (3 x)

sec (b) = \frac{1}{2}

2 cos (2 x) = sin (2 x)

0.322 = sin (3.92232 \cdot t)

cos (x) tan^{2} (x) = 3 cos (x), 0 \leq x < 2 π

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