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

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

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2-sin^2(x)=2cos^2(x/2)

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

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

Solution steps

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

Subtract

2 cos^{2} (\frac{x}{2})

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = 0

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

sec (\frac{θ}{5}) = 10

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

cos (θ) = \frac{15}{17}

3 sec^{2} (x) tan (x) = 4 tan (x)

csc^{2} (θ) = cot (θ) + 1

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