What is the general solution for 5cos(x)+5sin(x)tan(x)=10 ?

The general solution for 5cos(x)+5sin(x)tan(x)=10 is x= pi/3+2pin,x=(5pi)/3+2pin

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5cos(x)+5sin(x)tan(x)=10

5 cos (x) + 5 sin (x) tan (x) = 10

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

Solution steps

5 cos (x) + 5 sin (x) tan (x) = 10

Subtract

10

from both sides

5 cos (x) + 5 sin (x) tan (x) - 10 = 0

Rewrite using trig identities

- 10 + \frac{5}{cos ( x )} = 0

Multiply both sides by

cos (x)

- 10 cos (x) + 5 = 0

Move

5

to the right side

- 10 cos (x) = - 5

Divide both sides by

- 10

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 (x) = 0.33

2 cos (2 x) = - 1

3 sin (x) + cos^{2} (x) = 2

5 sin (2 θ) - 7 sin (θ) = 0

cos (θ) = \frac{3}{3}

What is the general solution for 5cos(x)+5sin(x)tan(x)=10 ?
The general solution for 5cos(x)+5sin(x)tan(x)=10 is x= pi/3+2pin,x=(5pi)/3+2pin