sqrt(3)tan(3θ)-1=0,0<= θ<= 2pi

Solution

3 tan (3 θ) - 1 = 0, 0 \leq θ \leq 2 π

θ = \frac{π}{18}, θ = \frac{7 π}{18}, θ = \frac{13 π}{18}, θ = \frac{19 π}{18}, θ = \frac{25 π}{18}

Solution steps

3 tan (3 θ) - 1 = 0, 0 \leq θ \leq 2 π

Move

1

to the right side

3 tan (3 θ) = 1

Divide both sides by

3

tan (3 θ) = \frac{3}{3}

General solutions for

tan (3 θ) = \frac{3}{3}

3 θ = \frac{π}{6} + πn

Solve

3 θ = \frac{π}{6} + πn : θ = \frac{π}{18} + \frac{πn}{3}

θ = \frac{π}{18} + \frac{πn}{3}

Solutions for the range

0 \leq θ \leq 2 π

θ = \frac{π}{18}, θ = \frac{7 π}{18}, θ = \frac{13 π}{18}, θ = \frac{19 π}{18}, θ = \frac{25 π}{18}

(cot (θ) + 1) (csc (θ) - 1) = 0

2 sin (x) cos (x) = 1

cos (x) sin (x) + 2 sin (x) = 0

cos (x) sin (x) = - sin (x)

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