What is the general solution for 15cot^2(x)=5 ?

The general solution for 15cot^2(x)=5 is x=1.04719…+pin,x=2.09439…+pin

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15cot^2(x)=5

15 cot^{2} (x) = 5

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

Solution steps

15 cot^{2} (x) = 5

Solve by substitution

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

cot (x) = \frac{1}{3} : x = arccot (\frac{1}{3}) + πn

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

Combine all the solutions

x = arccot (\frac{1}{3}) + πn, x = arccot (- \frac{1}{3}) + πn

Show solutions in decimal form

x = 1.04719 \dots + πn, x = 2.09439 \dots + πn

cos (2 x) - sin (x) = 1, 0 \leq x < 2 π

sec^{2} (x) + 5 sec (x) - 14 = 0

3 cos^{2} (x) = 1

cos (θ) = - \frac{7}{8}, csc (θ)

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

What is the general solution for 15cot^2(x)=5 ?
The general solution for 15cot^2(x)=5 is x=1.04719…+pin,x=2.09439…+pin