What is the general solution for tan^2(x)+cot^2(x)=1 ?

The general solution for tan^2(x)+cot^2(x)=1 is No Solution for x\in\mathbb{R}

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tan^2(x)+cot^2(x)=1

tan^{2} (x) + cot^{2} (x) = 1

No Solution for x \in R

Solution steps

tan^{2} (x) + cot^{2} (x) = 1

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = \frac{3}{2} + \frac{1}{2} i, cot (x) = - \frac{3}{2} - \frac{1}{2} i, cot (x) = - \frac{3}{2} + \frac{1}{2} i, cot (x) = \frac{3}{2} - \frac{1}{2} i

cot (x) = \frac{3}{2} + \frac{1}{2} i :

No Solution

cot (x) = - \frac{3}{2} - \frac{1}{2} i :

No Solution

cot (x) = - \frac{3}{2} + \frac{1}{2} i :

No Solution

cot (x) = \frac{3}{2} - \frac{1}{2} i :

No Solution

Combine all the solutions

No Solution for x \in R

4 sin (θ) = - 4 cos (θ)

- 3 sin (a) - 2 = sin (a) - 2

tan (A) = 1

3 sec^{2} (x) + 2 tan (x) - 23 = 0

sin (x) (1 - 2 cos (x)) = 0

What is the general solution for tan^2(x)+cot^2(x)=1 ?
The general solution for tan^2(x)+cot^2(x)=1 is No Solution for x\in\mathbb{R}