What is the general solution for 7cos(x)+7sin(x)tan(x)=14 ?

The general solution for 7cos(x)+7sin(x)tan(x)=14 is x= pi/3+2pin,x=(5pi)/3+2pin

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7cos(x)+7sin(x)tan(x)=14

7 cos (x) + 7 sin (x) tan (x) = 14

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

Solution steps

7 cos (x) + 7 sin (x) tan (x) = 14

Subtract

14

from both sides

7 cos (x) + 7 sin (x) tan (x) - 14 = 0

Rewrite using trig identities

- 14 + \frac{7}{cos ( x )} = 0

Multiply both sides by

cos (x)

- 14 cos (x) + 7 = 0

Move

7

to the right side

- 14 cos (x) = - 7

Divide both sides by

- 14

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

cot (θ) + 5 csc (θ) = 6

3 csc^{2} (x) + 2 csc (x) = 0

7 sin (2 x) sin (x) = 7 cos (x)

csc (x) + cot (x) = 3

sin^{2} (x) - sin (x) + 1 = cos^{2} (x)

What is the general solution for 7cos(x)+7sin(x)tan(x)=14 ?
The general solution for 7cos(x)+7sin(x)tan(x)=14 is x= pi/3+2pin,x=(5pi)/3+2pin