What is the general solution for cos(x)tan(x)-2cos^2(x)=-1 ?

The general solution for cos(x)tan(x)-2cos^2(x)=-1 is x= pi/6+2pin,x=(5pi)/6+2pin

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cos(x)tan(x)-2cos^2(x)=-1

cos (x) tan (x) - 2 cos^{2} (x) = - 1

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

Solution steps

cos (x) tan (x) - 2 cos^{2} (x) = - 1

Subtract

- 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = - 1

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

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

Since the equation is undefined for:

\frac{3 π}{2} + 2 πn

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

3 cot (\frac{1}{4} x) = 1

2 sin (\frac{π}{4} - x) + 3 = 0

3.1 = 48.1 (1 - cos (\frac{28.66 x}{48.1}))

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

2 cos^{2} (x) + 6 = 7

What is the general solution for cos(x)tan(x)-2cos^2(x)=-1 ?
The general solution for cos(x)tan(x)-2cos^2(x)=-1 is x= pi/6+2pin,x=(5pi)/6+2pin