What is the general solution for tan^2(x)+cot^2(x)-2=0 ?

The general solution for tan^2(x)+cot^2(x)-2=0 is x= pi/4+pin,x=(3pi)/4+pin

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tan^2(x)+cot^2(x)-2=0

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

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

Solution steps

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

Rewrite using trig identities

- 2 + cot^{2} (x) + \frac{1}{cot ^{2} ( x )} = 0

Solve by substitution

cot (x) = 1, cot (x) = - 1

cot (x) = 1 : x = \frac{π}{4} + πn

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

Combine all the solutions

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

12 sin (C) + 6 = 5 sin (C) + 6

10 sin (t) cos (t) = - 6 sin (t)

sin (2 x) = \frac{1}{2}

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

2 + 3 tan (x) = 3

What is the general solution for tan^2(x)+cot^2(x)-2=0 ?
The general solution for tan^2(x)+cot^2(x)-2=0 is x= pi/4+pin,x=(3pi)/4+pin