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

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

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cos(x)tan(x)+sin(x)=2cos(x)

cos (x) tan (x) + sin (x) = 2 cos (x)

x = \frac{π}{4} + πn

Solution steps

cos (x) tan (x) + sin (x) = 2 cos (x)

Subtract

2 cos (x)

from both sides

cos (x) tan (x) + sin (x) - 2 cos (x) = 0

Rewrite using trig identities

- 2 + 2 tan (x) = 0

Move

2

to the right side

2 tan (x) = 2

Divide both sides by

2

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

cos (x) + sin (x) = \frac{6}{2}

6 tan^{2} (x) - 2 = 0

tan (x) = \infty

2 arctanh (\frac{( x - 2 )}{( x + 1 )}) = ln (2)

tan (x) = - 1.5

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