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

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

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cos(2θ)=11sin(θ)-5

cos (2 θ) = 11 sin (θ) - 5

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

Solution steps

cos (2 θ) = 11 sin (θ) - 5

Subtract

11 sin (θ) - 5

from both sides

cos (2 θ) - 11 sin (θ) + 5 = 0

Rewrite using trig identities

6 - 11 sin (θ) - 2 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = - 6, sin (θ) = \frac{1}{2}

sin (θ) = - 6 :

No Solution

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

Combine all the solutions

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

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

x, sec (x) = - 3.5

4 tan (θ) = 3 + tan (θ)

tan (2 x) + sec (2 x) = 10

t, sin (t) = 0

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