What is the general solution for cos(30+x)-sin(x)=0 ?

The general solution for cos(30+x)-sin(x)=0 is x=30+180n

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cos(30+x)-sin(x)=0

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

x = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

\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 = 3 0^{\circ} + 18 0^{\circ} n

53 cos (x) - 10 sin (x) cos (x) = 0

tan (x) = \frac{5}{20}

cos (x) (1 + 2 sin (x)) = 0

tan (θ) = \frac{6}{5}, π < θ < \frac{3 π}{2}

sin (x) + sin (9 0^{\circ} - x) = sin (9 0^{\circ})

What is the general solution for cos(30+x)-sin(x)=0 ?
The general solution for cos(30+x)-sin(x)=0 is x=30+180n