What is the general solution for 4cos(x)+4sin(x)tan(x)=8 ?

The general solution for 4cos(x)+4sin(x)tan(x)=8 is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos(x)+4sin(x)tan(x)=8

4 cos (x) + 4 sin (x) tan (x) = 8

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

Solution steps

4 cos (x) + 4 sin (x) tan (x) = 8

Subtract

8

from both sides

4 cos (x) + 4 sin (x) tan (x) - 8 = 0

Rewrite using trig identities

- 8 + \frac{4}{cos ( x )} = 0

Multiply both sides by

cos (x)

- 8 cos (x) + 4 = 0

Move

4

to the right side

- 8 cos (x) = - 4

Divide both sides by

- 8

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

2 tan^{2} (x) - 3 sec (x) = 0

5 sin (x) tan (x) - 4 tan (x) = 0

5 cos (5 x) = 0

7 cos (x) - 7 sin (x) = 0

9 sin (x) cos (x) = 5 cos (x)

What is the general solution for 4cos(x)+4sin(x)tan(x)=8 ?
The general solution for 4cos(x)+4sin(x)tan(x)=8 is x= pi/3+2pin,x=(5pi)/3+2pin