What is the general solution for tan^{22}(x)=sec^2(x)-1 ?

The general solution for tan^{22}(x)=sec^2(x)-1 is x=pin,x= pi/4+pin,x=(3pi)/4+pin

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tan^{22}(x)=sec^2(x)-1

tan^{22} (x) = sec^{2} (x) - 1

x = πn, x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

tan^{22} (x) = sec^{2} (x) - 1

Subtract

sec^{2} (x) - 1

from both sides

tan^{22} (x) - sec^{2} (x) + 1 = 0

Rewrite using trig identities

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

Solve by substitution

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

tan (x) = 0 : x = πn

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = πn, x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

tan^{4} (x) + tan^{2} (x) = tan (x)

sin^{4} (x) + sin^{2} (x) = sin^{6} (x)

cos (a) = \frac{- 11}{14}

x, sin (\frac{x}{x}) = 0.7

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

What is the general solution for tan^{22}(x)=sec^2(x)-1 ?
The general solution for tan^{22}(x)=sec^2(x)-1 is x=pin,x= pi/4+pin,x=(3pi)/4+pin