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

The general solution for cos(pi/6+x)+sin(pi/3+x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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cos(pi/6+x)+sin(pi/3+x)=0

cos (\frac{π}{6} + x) + sin (\frac{π}{3} + x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

cos (\frac{π}{6} + x) + sin (\frac{π}{3} + x) = 0

Rewrite using trig identities

3 cos (x) = 0

Divide both sides by

3

cos (x) = 0

General solutions for

cos (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2.55 = \frac{1}{tan ( x )}

tan (5 x) = cot (x)

\frac{1}{4} sin (8 x) = - \frac{1}{8}, 2 cos (8 x) = 3

sin (x) - sin (2 x) = 0, 0 \leq x < 2 π

sin (2 x) = \frac{- 2 6}{7}

What is the general solution for cos(pi/6+x)+sin(pi/3+x)=0 ?
The general solution for cos(pi/6+x)+sin(pi/3+x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin