What is the general solution for cos^{22}(x)+sin^2(x)-1=0 ?

The general solution for cos^{22}(x)+sin^2(x)-1=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x=2pin,x=pi+2pin

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cos^{22}(x)+sin^2(x)-1=0

cos^{22} (x) + sin^{2} (x) - 1 = 0

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

Solution steps

cos^{22} (x) + sin^{2} (x) - 1 = 0

Rewrite using trig identities

cos^{22} (x) - cos^{2} (x) = 0

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

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

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

5 sin (2 x) + 9 sin (x) = 0

4 sin (x) - 6 cos (x) = 3

4 cos (x) = cos^{3} (x)

What is the general solution for cos^{22}(x)+sin^2(x)-1=0 ?
The general solution for cos^{22}(x)+sin^2(x)-1=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x=2pin,x=pi+2pin