What is the general solution for 8(cos(x))^2-6sin(x)=3 ?

The general solution for 8(cos(x))^2-6sin(x)=3 is x= pi/6+2pin,x=(5pi)/6+2pin

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8(cos(x))^2-6sin(x)=3

8 (cos (x))^{2} - 6 sin (x) = 3

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

Solution steps

8 (cos (x))^{2} - 6 sin (x) = 3

Subtract

3

from both sides

8 cos^{2} (x) - 6 sin (x) - 3 = 0

Rewrite using trig identities

5 - 6 sin (x) - 8 sin^{2} (x) = 0

Solve by substitution

sin (x) = - \frac{5}{4}, sin (x) = \frac{1}{2}

sin (x) = - \frac{5}{4} :

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

sin (x) = \frac{- tan ( x )}{2}

2 sin (3 θ) - 1 = 0, 0 \leq θ \leq 2 π

sin (θ) = - \frac{5}{7}

cos (x) sin (x) = sin (x)

sec^{2} (x) - 1 = 1

What is the general solution for 8(cos(x))^2-6sin(x)=3 ?
The general solution for 8(cos(x))^2-6sin(x)=3 is x= pi/6+2pin,x=(5pi)/6+2pin