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

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

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

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

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

Solution steps

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

Subtract

2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 2, cos (x) = 0

cos (x) = 2 :

No Solution

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

Combine all the solutions

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

2 cos^{2} (x) - 2 cos (2 x) = 1

12 cot^{2} (x) = 4

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

5 sin^{2} (θ) + 2 sin (θ) = 0

cos (θ) cos (3 θ) - sin (θ) sin (3 θ) = 0

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