What is the general solution for cos(x-pi/6)-sin(x)=0 ?

The general solution for cos(x-pi/6)-sin(x)=0 is x= pi/3+pin

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cos(x-pi/6)-sin(x)=0

cos (x - \frac{π}{6}) - sin (x) = 0

x = \frac{π}{3} + πn

Solution steps

cos (x - \frac{π}{6}) - sin (x) = 0

Rewrite using trig identities

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

Simplify

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

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

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

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

Rewrite using trig identities

3 - tan (x) = 0

Move

3

to the right side

- tan (x) = - 3

Divide both sides by

- 1

tan (x) = 3

General solutions for

tan (x) = 3

x = \frac{π}{3} + πn

2 + cos^{2} (x) = - 3 cos (x)

6 sec^{2} (x) + tan (x) - 7 = 0

4 \cdot sin^{2} (x) = 3

cos (B) = \frac{2}{3}

tan (θ) sin (θ) = 3 sin (θ)

What is the general solution for cos(x-pi/6)-sin(x)=0 ?
The general solution for cos(x-pi/6)-sin(x)=0 is x= pi/3+pin