What is the general solution for cos^2(x)+sin^2(2x)=0 ?

The general solution for cos^2(x)+sin^2(2x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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cos^2(x)+sin^2(2x)=0

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

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

Solution steps

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

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

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

No Solution

Combine all the solutions

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

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

42 - 25 cos (x) = 31

2 sec^{2} (x) = 5 tan (x)

cos^{2} (2 x) - 3 sin^{2} (x) - 1 = 0

sin (- t) = \frac{3}{10}

What is the general solution for cos^2(x)+sin^2(2x)=0 ?
The general solution for cos^2(x)+sin^2(2x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin