What is the general solution for 8cos(x)+8sin(x)tan(x)=16 ?

The general solution for 8cos(x)+8sin(x)tan(x)=16 is x= pi/3+2pin,x=(5pi)/3+2pin

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8cos(x)+8sin(x)tan(x)=16

8 cos (x) + 8 sin (x) tan (x) = 16

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

Solution steps

8 cos (x) + 8 sin (x) tan (x) = 16

Subtract

16

from both sides

8 cos (x) + 8 sin (x) tan (x) - 16 = 0

Rewrite using trig identities

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

Multiply both sides by

cos (x)

- 16 cos (x) + 8 = 0

Move

8

to the right side

- 16 cos (x) = - 8

Divide both sides by

- 16

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

(sin (2 x) - 1) (2 sin (2 x) - 1) = 0

2 cos^{2} (x) - cos (x) = 2 - sec (x)

sin^{4} (x) - cos^{4} (x) = \frac{1}{2}

x, y = tan (x)

sin (θ) = - 2

What is the general solution for 8cos(x)+8sin(x)tan(x)=16 ?
The general solution for 8cos(x)+8sin(x)tan(x)=16 is x= pi/3+2pin,x=(5pi)/3+2pin