What is the general solution for 4(cos(x))^2=5-4sin(x) ?

The general solution for 4(cos(x))^2=5-4sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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4(cos(x))^2=5-4sin(x)

4 (cos (x))^{2} = 5 - 4 sin (x)

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

Solution steps

4 (cos (x))^{2} = 5 - 4 sin (x)

Subtract

5 - 4 sin (x)

from both sides

4 cos^{2} (x) - 5 + 4 sin (x) = 0

Rewrite using trig identities

- 1 + 4 sin (x) - 4 sin^{2} (x) = 0

Solve by substitution

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

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

tan (2 t) = 1

21 = 3 \cdot 2 \cdot 25 sin (x) + 9.8 \cdot 3 \cdot 2 \cdot 3 \cdot 2 \cdot 0.5

sin (2 x) = \frac{( 3 m - 8 )}{6}

cos (x) (18 - 122) = 12 + 63

cos (2 x + \frac{π}{3}) = \frac{3}{2}, 0 \leq x \leq 2 π

What is the general solution for 4(cos(x))^2=5-4sin(x) ?
The general solution for 4(cos(x))^2=5-4sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin