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

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

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

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

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

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

cos^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

cos (x) = 0

General solutions for

cos (x) = 0

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

\frac{sin ^{2} ( a ) + 1}{tan ^{2} ( a )} = 1

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

4 cos^{2} (x) = sin^{2} (x) + 3

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

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

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