Identify the solutions to the below equation on the interval \$0 le x < 2pi\$.

\$ 1/(cosx - 1) - 1/(2cosx - 1) = - 1/(2cos^2 x - 3cosx + 1) \$

A) \$x = pi/6 \$

B) \$x = pi \$

C) \$x = pi/4 \$

D) \$x = pi/2 \$

Identify the general solution to the equation:

\$ (4 cosx)/(sinx) + 3/(sin^2 x) = (6 cosx sinx)/(cos^2 x - 1)\$.

A) \$x = arccos (- 3) + kpi, arccos (- 1/3) + kpi\$

B) \$x = arccot (- 3) + kpi, arccot (- 1/3) + kpi\$

C) \$x = arctan (- 3) + kpi, arctan (- 1/3) + kpi\$

D) \$x = arctan ( 3) + kpi, arctan (1/3) + kpi\$

Identify the solutions to the equation \$ tan(x - pi) + tan(x + pi/4) = 0\$ on the interval \$ - pi/2 le x le pi/2\$.

A) \$ arctan( 1 + \sqrt2)\$ and \$ arccot(1 + \sqrt2)\$

B) \$ arccot( 1 - \sqrt2)\$ and \$ arccot(1 + \sqrt2)\$

C) \$ arctan( - 1 - \sqrt2)\$ and \$ arctan(- 1 + \sqrt2)\$

D) \$ arctan( 1 - \sqrt2)\$ and \$ arctan(1 + \sqrt2)\$

Identify the solutions to the equation (tan 2x)(sin 2x) = 0 on the interval \$0 le x < 2pi\$.

A) \$ 0, pi\$

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

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

D) \$ (5pi)/3, (7pi)/3\$

Identify the solutions to the equation \$ tan (θ/2) - 1 = 0\$ on the interval \$0 le x < 2pi\$.

A) \$ pi/2\$

B) \$ pi/6 \$

C) \$pi/4 \$

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

Identify the solutions to the below equation on the interval
0 ≤ x < 2π.
\$cot^3 x - cot x + csc^2 x - 2 = 0\$

A) \$pi/4, (3pi)/4, (5pi)/4,(7pi)/4\$

B) \$pi/4, (9pi)/4, (5pi)/4,(7pi)/4\$

C) \$(2pi)/4, (3pi)/4, (5pi)/4,(7pi)/4\$

D) \$(2pi)/4, (3pi)/4, (5pi)/4,(11pi)/4\$

Identify the general solution to the equation: \$sin^4(x) + 4cos^2(x) = 0\$.

A) No real solutions

B) Zero

C) Infinity

D) Real solutions

Slove the equation on the interval 0 ≤ x < 2π: secx - 1 - tanx = tanx.

A) \$x = 0 , cos^-1(5/3)\$

B) \$x = 0 , cos^-1(-3/5)\$

C) \$x = 0 , cos^-1(- 5/3)\$

D) \$x = 0 , cos^-1(3/5)\$

Identify the solutions to the equation \$sin (x - (pi)/3) = 0\$ on the interval 0 ≤ x < 2π.

A) \$pi/3, (4pi)/3, (5pi)/3\$

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

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

D) \$(2pi)/3, (4pi)/3, (5pi)/3, (7pi)/3\$

Identify the general solution to the equation: \$3 sec^2(θ) + 4 tan(θ) = 5 (sec^2(θ) - 1)\$.

A) \$tan^-1(1 - \sqrt(2)/10) + kπ , tan^-1(1 + \sqrt(2)/10) + kπ \$

B) \$tan^-1(1 - \sqrt(10)/5) + kπ , tan^-1(1 + \sqrt(10)/5) + kπ \$

C) \$tan^-1(1 - \sqrt(5)/10) + kπ , tan^-1(1 + \sqrt(5)/10) + kπ \$

D) \$tan^-1(1 - \sqrt(10)/2) + kπ , tan^-1(1 + \sqrt(10)/2) + kπ \$