What is the general solution for sqrt(1+cot^2(x))=8 ?

The general solution for sqrt(1+cot^2(x))=8 is x=0.12532…+pin,x=3.01626…+pin

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sqrt(1+cot^2(x))=8

1 + cot^{2} (x) = 8

x = 0.12532 \dots + πn, x = 3.01626 \dots + πn

Solution steps

1 + cot^{2} (x) = 8

Solve by substitution

cot (x) = 37, cot (x) = - 37

cot (x) = 37 : x = arccot (37) + πn

cot (x) = - 37 : x = arccot (- 37) + πn

Combine all the solutions

x = arccot (37) + πn, x = arccot (- 37) + πn

Show solutions in decimal form

x = 0.12532 \dots + πn, x = 3.01626 \dots + πn

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

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

cos (θ) = - \frac{2}{5}, tan (2 θ)

sin (x + \frac{π}{6}) = \frac{2}{2}

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

What is the general solution for sqrt(1+cot^2(x))=8 ?
The general solution for sqrt(1+cot^2(x))=8 is x=0.12532…+pin,x=3.01626…+pin