What is the general solution for 7tan(x)cos(x)=2cos(x) ?

The general solution for 7tan(x)cos(x)=2cos(x) is x=0.27829…+pin

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7tan(x)cos(x)=2cos(x)

7 tan (x) cos (x) = 2 cos (x)

x = 0.27829 \dots + πn

Solution steps

7 tan (x) cos (x) = 2 cos (x)

Subtract

2 cos (x)

from both sides

7 tan (x) cos (x) - 2 cos (x) = 0

Factor

7 tan (x) cos (x) - 2 cos (x) : cos (x) (7 tan (x) - 2)

cos (x) (7 tan (x) - 2) = 0

Solving each part separately

cos (x) = 0 or 7 tan (x) - 2 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

7 tan (x) - 2 = 0 : x = arctan (\frac{2}{7}) + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arctan (\frac{2}{7}) + πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

x = arctan (\frac{2}{7}) + πn

Show solutions in decimal form

x = 0.27829 \dots + πn

sin (4 θ) = - \frac{3}{2}

1 = 6 cos (x)

x, sec (x) = 0

sin (\frac{x}{3}) = \frac{3}{2}

2 cos (θ) sin (θ) - cos (θ) = 0

What is the general solution for 7tan(x)cos(x)=2cos(x) ?
The general solution for 7tan(x)cos(x)=2cos(x) is x=0.27829…+pin