What is the general solution for solvefor x,p+3q=5z+tan(y-3x) ?

The general solution for solvefor x,p+3q=5z+tan(y-3x) is x=-(arctan(p+3q-5z))/3-(pin)/3+y/3

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solvefor x,p+3q=5z+tan(y-3x)

solve for

x, p + 3 q = 5 z + tan (y - 3 x)

x = - \frac{arctan ( p + 3 q - 5 z )}{3} - \frac{πn}{3} + \frac{y}{3}

Solution steps

p + 3 q = 5 z + tan (y - 3 x)

Switch sides

5 z + tan (y - 3 x) = p + 3 q

Move

5 z

to the right side

tan (y - 3 x) = p + 3 q - 5 z

Apply trig inverse properties

y - 3 x = arctan (p + 3 q - 5 z) + πn

Solve

y - 3 x = arctan (p + 3 q - 5 z) + πn : x = - \frac{arctan ( p + 3 q - 5 z )}{3} - \frac{πn}{3} + \frac{y}{3}

x = - \frac{arctan ( p + 3 q - 5 z )}{3} - \frac{πn}{3} + \frac{y}{3}

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

sec (x) = 2, 0 \leq x < 2 π

3 cot (θ) - 8 = - 11

2 cos (\frac{π}{4} - x) = 1

sin (θ) = \frac{56}{65}

What is the general solution for solvefor x,p+3q=5z+tan(y-3x) ?
The general solution for solvefor x,p+3q=5z+tan(y-3x) is x=-(arctan(p+3q-5z))/3-(pin)/3+y/3