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

The general solution for 1+tan^2(x)=cot^2(x) is x=0.66623…+pin,x=2.47535…+pin

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

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

x = 0.66623 \dots + πn, x = 2.47535 \dots + πn

Solution steps

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

Subtract

cot^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cot (x) = i \frac{- 1 + 5}{2}, cot (x) = - i \frac{- 1 + 5}{2}, cot (x) = \frac{1 + 5}{2}, cot (x) = - \frac{1 + 5}{2}

cot (x) = i \frac{- 1 + 5}{2} :

No Solution

cot (x) = - i \frac{- 1 + 5}{2} :

No Solution

cot (x) = \frac{1 + 5}{2} : x = arccot \frac{1 + 5}{2} + πn

cot (x) = - \frac{1 + 5}{2} : x = arccot - \frac{1 + 5}{2} + πn

Combine all the solutions

x = arccot \frac{1 + 5}{2} + πn, x = arccot - \frac{1 + 5}{2} + πn

Show solutions in decimal form

x = 0.66623 \dots + πn, x = 2.47535 \dots + πn

1 - 4 tan (3 x + 1) = 17

sin (x) cos (x) + sin (x) = 3 cos^{2} (x) + 3 cos (x)

2 - 2 sin^{2} (x) = - 3 cos (x) + 2

4 tan (θ) + 7 = 0

arctan (x) + arctan (3 x) + arctan (7 x) = 18 0^{\circ}

What is the general solution for 1+tan^2(x)=cot^2(x) ?
The general solution for 1+tan^2(x)=cot^2(x) is x=0.66623…+pin,x=2.47535…+pin