Solve the equation: \$sin2x + 2 cosx sinx = \sqrt3\$.

A) \$ pi/3, pi/6 \$

B) \$ pi/2, 0\$

C) \$ pi/4, pi/2 \$

D) \$ 2pi, pi \$

Solve the equation exactly: \$3sinθ + 3 = 2cos^2(θ)\$ , 0 ≤ θ <2π.

A) \$(pi)/6 , (11pi)/6, (3pi)/2\$

B) \$(-7pi)/6 , (-11pi)/6, (3pi)/2\$

C) \$(pi)/6 , (11pi)/6, (pi)/2\$

D) \$(7pi)/6 , (11pi)/6, (3pi)/2\$

Solve exactly: \$sin(2x) = 1/2\$ on (0,2π).

A) \$(13pi)/12, (12pi)/13\$

B) \$(13pi)/12, (17pi)/12\$

C) \$(13pi)/12, (12pi)/17\$

D) \$(12pi)/13, (17pi)/12\$

Determine the exact solutions for the equation \$ 2cos^2θ - 3cosθ + 1 = 0\$ within the interval \$0 le θ < 2π \$.

A) \$ pi, pi/6, (7pi)/3 \$

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

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

D) \$ 0, 2pi, pi/3, (5pi)/3 \$

Identify the general solution to the equation: 3(tan(2x) - 4) + 9 = 0.

A) \$ x = pi + npi\$

B) \$ x = pi/2 + (3npi)/2\$

C) \$ x = pi/8 + (npi)/2\$

D) \$ x = pi/3 + (npi)/3\$