What is the general solution for sin^2(x)+4cos^2(x)=1 ?

The general solution for sin^2(x)+4cos^2(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin

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sin^2(x)+4cos^2(x)=1

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

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

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

3 cos^{2} (x) = 0

Divide both sides by

3

cos (x) = 0

General solutions for

cos (x) = 0

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

4 cos (x^{2}) - 3 = 0

sin (x) + 1 = 0, 0 \leq x < 2 π

θ, sin^{2} (θ) = \frac{1}{4}

cot (θ) = 3, 0 \leq θ < 2 π

(2 cos (2 θ)) = 2

What is the general solution for sin^2(x)+4cos^2(x)=1 ?
The general solution for sin^2(x)+4cos^2(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin