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

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

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

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

x = 2 πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = 2 πn

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

cos^{2} (x) + sin^{2} (x) - 2 sin (x) = 0, 0 \leq x \leq 2 π

cot (A) = \frac{24}{7}

23 sec (θ) + 4 = 0

3 sin (x) = 2

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