What is the general solution for 10cos(θ)=4sin^2(θ)+2 ?

The general solution for 10cos(θ)=4sin^2(θ)+2 is θ= pi/3+2pin,θ=(5pi)/3+2pin

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10cos(θ)=4sin^2(θ)+2

10 cos (θ) = 4 sin^{2} (θ) + 2

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

Solution steps

10 cos (θ) = 4 sin^{2} (θ) + 2

Subtract

4 sin^{2} (θ) + 2

from both sides

10 cos (θ) - 4 sin^{2} (θ) - 2 = 0

Rewrite using trig identities

- 6 + 10 cos (θ) + 4 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 3

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

cos (θ) = - 3 :

No Solution

Combine all the solutions

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

\frac{tan ^{2} ( x ) ( 1 + cot ^{2} ( x ) )}{sec ( x )} = cos (x)

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

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

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

csc (θ) = (1.201)

What is the general solution for 10cos(θ)=4sin^2(θ)+2 ?
The general solution for 10cos(θ)=4sin^2(θ)+2 is θ= pi/3+2pin,θ=(5pi)/3+2pin