What is the general solution for cos(x+pi/6)=sin(x) ?

The general solution for cos(x+pi/6)=sin(x) is x= pi/6+pin

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cos(x+pi/6)=sin(x)

cos (x + \frac{π}{6}) = sin (x)

x = \frac{π}{6} + πn

Solution steps

cos (x + \frac{π}{6}) = sin (x)

Rewrite using trig identities

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

Subtract

sin (x)

from both sides

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

Simplify

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

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

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

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

Rewrite using trig identities

3 - 3 tan (x) = 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 = \frac{π}{6} + πn

sin (θ) = - \frac{1}{5}

5 cot (x) - 5 = 0

2 - \frac{1}{2} sin (3 x + 330) = \frac{8 - 3}{4}

2 sin^{2} (x) + sin (x) + 1 = 0

sin (x) = \frac{20}{29}

What is the general solution for cos(x+pi/6)=sin(x) ?
The general solution for cos(x+pi/6)=sin(x) is x= pi/6+pin