What is the general solution for 4cos(x)-2=2tan(x)cot(x)-sec(x) ?

The general solution for 4cos(x)-2=2tan(x)cot(x)-sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos(x)-2=2tan(x)cot(x)-sec(x)

4 cos (x) - 2 = 2 tan (x) cot (x) - sec (x)

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

Solution steps

4 cos (x) - 2 = 2 tan (x) cot (x) - sec (x)

Subtract

2 tan (x) cot (x) - sec (x)

from both sides

4 cos (x) - 2 - 2 tan (x) cot (x) + sec (x) = 0

Express with sin, cos

\frac{1 - 4 cos ( x ) + 4 cos ^{2} ( x )}{cos ( x )} = 0

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

1 - 4 cos (x) + 4 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

11 (1 - cos (θ)) = sin^{2} (θ)

cos^{2} (x) - \frac{1}{2} = 0, 0 \leq x \leq 2 π

x, tan (x) = tan (y)

4 cos (θ) + 3 = 0

2 cos^{2} (x) + 1 = 3 cos (x), 0 \leq x \leq 2 π

What is the general solution for 4cos(x)-2=2tan(x)cot(x)-sec(x) ?
The general solution for 4cos(x)-2=2tan(x)cot(x)-sec(x) is x= pi/3+2pin,x=(5pi)/3+2pin