What is the general solution for 25cot^2(x)-1=0 ?

The general solution for 25cot^2(x)-1=0 is x=1.37340…+pin,x=1.76819…+pin

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25cot^2(x)-1=0

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

x = 1.37340 \dots + πn, x = 1.76819 \dots + πn

Solution steps

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

Solve by substitution

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

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

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.37340 \dots + πn, x = 1.76819 \dots + πn

\frac{3}{2} = - \frac{1}{2} \cdot sin (θ)

sin (θ) = 0.27, 0 \leq θ < 2 π

tan (x) = 0.96

tan (x) = 0.87

4 sec (θ) + 6 = - 2, 0 \leq θ < 2 π

What is the general solution for 25cot^2(x)-1=0 ?
The general solution for 25cot^2(x)-1=0 is x=1.37340…+pin,x=1.76819…+pin