What is the general solution for cos(2x)=11sin(x)-5 ?

The general solution for cos(2x)=11sin(x)-5 is x= pi/6+2pin,x=(5pi)/6+2pin

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cos(2x)=11sin(x)-5

cos (2 x) = 11 sin (x) - 5

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

Solution steps

cos (2 x) = 11 sin (x) - 5

Subtract

11 sin (x) - 5

from both sides

cos (2 x) - 11 sin (x) + 5 = 0

Rewrite using trig identities

6 - 11 sin (x) - 2 sin^{2} (x) = 0

Solve by substitution

sin (x) = - 6, sin (x) = \frac{1}{2}

sin (x) = - 6 :

No Solution

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

Combine all the solutions

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

x, z = \frac{4}{π} arctan (x y)

sin^{2} (x) cot (x) - cot (x) = 0

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

sin (x) = \frac{- 1}{3}

cos (\frac{x}{4}) = \frac{1}{2}

What is the general solution for cos(2x)=11sin(x)-5 ?
The general solution for cos(2x)=11sin(x)-5 is x= pi/6+2pin,x=(5pi)/6+2pin