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

The general solution for 2cos(x)=cot(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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2cos(x)=cot(x)

2 cos (x) = cot (x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

2 cos (x) = cot (x)

Subtract

cot (x)

from both sides

2 cos (x) - cot (x) = 0

Express with sin, cos

\frac{- cos ( x ) + 2 cos ( x ) sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Factor

- cos (x) + 2 cos (x) sin (x) : cos (x) (2 sin (x) - 1)

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

Solving each part separately

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

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

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

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

cos (2 t) - cos (t) = - 0.5

sin^{2} (x) - cos (x) + 1 = 0

tan (2 x) = 2 sin (x)

sin (θ) - cos (θ) = \frac{2 + 3}{2}

What is the general solution for 2cos(x)=cot(x) ?
The general solution for 2cos(x)=cot(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin