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

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

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

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

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

Solution steps

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

Subtract

5

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

Combine all the solutions

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

cot (θ) + 1 = 0, (0, 2 π)

cos (θ) = \frac{4}{3.3 8 ^{2} + 4 ^{2}}

tan (x - 1 0^{\circ}) = - 0.1

2 (cos (x) + 3) = 5 + cos (x)

4 cos (3 x) - 1 = 2 sin (3 x) tan (3 x)

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