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

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

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

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

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

Solution steps

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

Subtract

\frac{5}{4}

from both sides

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

Simplify

cos^{2} (x) + sin (x) - \frac{5}{4} : \frac{4 cos ^{2} ( x ) + 4 sin ( x ) - 5}{4}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

\frac{8.87}{9.8} = sin (α) - 0.1 1 - sin^{2} (α)

tan (x) cos (x) + tan (x) = 0

sin (θ) = 508

2 = csc (x) cot (x)

sin^{2} (x) = 5

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