What is the general solution for tan^2(x)=cot^2(x) ?

The general solution for tan^2(x)=cot^2(x) is x= pi/4+pin,x=(3pi)/4+pin

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tan^2(x)=cot^2(x)

tan^{2} (x) = cot^{2} (x)

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

Solution steps

tan^{2} (x) = cot^{2} (x)

Subtract

cot^{2} (x)

from both sides

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

Factor

tan^{2} (x) - cot^{2} (x) : (tan (x) + cot (x)) (tan (x) - cot (x))

(tan (x) + cot (x)) (tan (x) - cot (x)) = 0

Solving each part separately

tan (x) + cot (x) = 0 or tan (x) - cot (x) = 0

tan (x) + cot (x) = 0 :

No Solution

tan (x) - cot (x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Combine all the solutions

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

x, cos (\frac{x}{2}) = - cos (2 x - 30)

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

cos (2 x - 1) = \frac{1}{2}

tan (a) = \frac{5}{3}

sin (x) = 0.43333333

What is the general solution for tan^2(x)=cot^2(x) ?
The general solution for tan^2(x)=cot^2(x) is x= pi/4+pin,x=(3pi)/4+pin