Find the solution to the equation \$"tanx" + 1/("tanx") = 1/2 \$.

A) \$ pi/4\$

B) No solutions

C) \$ pi/2\$

D) \$ pi\$

Solve the equation \$"cot"(θ/2)(1 - cos(θ)) = \sqrt2/2 \$, 0° ≤ θ < 180°.

A) \$ pi/2, (3pi)/2 \$

B) \$ pi/3, (4pi)/3 \$

C) \$ pi/4, (3pi)/4 \$

D) \$ 0, 2pi \$

Identify the general solution to the equation: \$cot^3 θ + 3 cot^2 θ + 6 = - 2 cot θ\$.

A) \$ θ = arctan(5/3) + 3kpi \$, such that k is an integer

B) \$ θ = arccot(- 1/3) + kpi \$, such that k is an integer

C) \$ θ = arccot(- 3 + \sqrt2) + 2kpi \$, such that k is an integer

D) \$ θ = arctan(- 1/3) + kpi \$, such that k is an integer

Identify the general solution to the equation: \$ tan^2 (x/3) + 4 tan (x/3) = 4\$.

A) \$x = 3arctan(-2 - 2\sqrt2)+ 3kpi, 3arctan(-2 + 2\sqrt2)+ 3kpi\$

B) \$x = arctan(-2 - 2\sqrt2)+ kpi, arctan(-2 + 2\sqrt2)+ kpi\$

C) \$\theta = arctan((-5-\sqrt13)/6), arctan((-5+\sqrt13)/6)\$

D) \$\theta = arctan((5-\sqrt1)/6), arctan((5+\sqrt1)/6)\$

Solve the equation \$2 sin(x/2) = 1\$.

A) \$ pi/3, (5pi)/3, (13pi)/3, (17pi)/3 \$

B) \$ pi/2, (3pi)/2, (4pi)/3, (5pi)/2 \$

C) \$ pi/4, (3pi)/4 \$

D) \$ 0, pi/2, pi, 2pi \$

Solve the equation exactly: \$tan^2θ + 6 tanθ −1 = 0\$, 0 ≤ θ < 2π.

A) 3.30 and 4.87

B) 3.20 and 4.87

C) 3.03 and 4.78

D) 3.20 and 4.77

Solve the equation exactly: \$4cot^2θ + 7cotθ + 3 = 0\$, 0 ≤ θ ≤ 2π..

A) \$(3pi)/4\$

B) \$(4pi)/3\$

C) \$-(3pi)/4\$

D) \$-(4pi)/3\$

Find the solution to the equation \$tan(2x) = 0\$ on (0, 2π).

A) \$(-3pi) , (-2pi)/3, (2pi)\$

B) \$(pi)/2, pi, (3pi)/2\$

C) \$(3pi) , (2pi)/3, (2pi)\$

D) \$(-pi) , (3pi)/2, (-2pi)\$

Identify the general solution to the equation: \$2(cos(3x) - 2) = 3(cos(3x) - 1)\$.

A) \$(pi)/3 - (2kpi)/3\$

B) \$(4pi)/3 - (2kpi)/3\$

C) \$(pi)/3 + (2kpi)/3\$

D) \$(4pi)/3 + (2kpi)/3\$

Solve the equation exactly: \$6cot^2θ + 7 cotθ + 1 = 0\$, 0 ≤ θ < 360.

A) 104°

B) 153°

C) 140°

D) 135°