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

The general solution for 3cos(x)+3sin(x)tan(x)=6 is x= pi/3+2pin,x=(5pi)/3+2pin

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3cos(x)+3sin(x)tan(x)=6

3 cos (x) + 3 sin (x) tan (x) = 6

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

3 cos (x) + 3 sin (x) tan (x) = 6

Subtract

6

from both sides

3 cos (x) + 3 sin (x) tan (x) - 6 = 0

Rewrite using trig identities

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

Multiply both sides by

cos (x)

- 6 cos (x) + 3 = 0

Move

3

to the right side

- 6 cos (x) = - 3

Divide both sides by

- 6

cos (x) = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

cos (x) = 0

Combine undefined points with solutions:

cos (x) = \frac{1}{2}

General solutions for

cos (x) = \frac{1}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

tan^{2} (2 x) - 1 = 0

3 sin (4 x) = - 6 sin (2 x)

2 sin (2 θ) - 3 = 0

2 sin^{2} (x) - sin (x) - 1 = 0, 0 \leq x \leq 2 π

4 cos (2 θ) + 12 = - 2 cos (θ) + 9

What is the general solution for 3cos(x)+3sin(x)tan(x)=6 ?
The general solution for 3cos(x)+3sin(x)tan(x)=6 is x= pi/3+2pin,x=(5pi)/3+2pin