Identify the solutions to the equation \$ 9 "cot"^4 "x" - 1 = 0\$ on the interval \$0 le x < 2pi\$.

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

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

C) \$ pi/6, (2pi)/3, (4pi)/3, (5pi)/6\$

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

Identify the solutions to the equation \$2("cos"^2 "x" + 4) - 9 = 0\$ on the interval
\$0 le "x" < 2pi\$.

A) \$ pi/2, (3pi)/2, (5pi)/2, (7pi)/2\$

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

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

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

Identify the general solution to the equation \$ (3 "sin"^2 "x" + 2 "sinx" - 5)/(sin^2 "x" + "sinx" - 2) = 0\$.

A) \$ pi/3\$

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

C) \$2 pi\$

D) No solutions

Prove that \$ "cot" 4"x"("sin" 5"x" + "sin" 3"x") = "cot" "x" ("sin" 5"x" - "sin"3"x")\$.

A) LHS = RHS

B) \$"LHS" ne "RHS"\$

C) \$"LHS" < "RHS"\$

D) \$"LHS" > "RHS"\$

Prove that \$ 2 "sin"^2 ((3pi)/4) + 2 "cos"^2 ((pi)/4) + 2 "sec"^2 ((pi)/3) = 10 \$.

A) Proved

B) Not proved

C) 0

D) 8

Solve for x in the interval [0, 2π]: \$"sin"⁡2"x" = \sqrt(3) "cosx"\$.

A) 30° 60° 75° 45°

B) 3.20 and 4.87

C) 3.03 and 4.78

D) 3.20 and 4.77

If \$5("tan"^2("x") - "cos"^2("x")) = 2"cosx" + 9\$ then find the value of cos4x is?

A) \$- 7/9\$

B) \$9/7\$

C) \$7/9\$

D) \$- 9/7\$

Solve the equation exactly: \$2"sin"^2(θ) - 5"sin"θ + 3 = 0\$, 0 ≤ θ ≤ 2π.

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

B) \$(pi)/2\$

C) \$pi\$

D) \$(4pi)/5\$

Solve the equation cot x = csc x, where 0 ≤ x < 2π.

A) Real solutions

B) Infinity

C) No real solutions

D) Zero

Identify the solutions to the equation \$"cos"2"x" - 2"sin"^2("x") = 0\$ on the interval 0 ≤ θ ≤ 2π.

A) \$pi/6, (5pi)/6, (13pi)/6, (11pi)/6\$

B) \$(5pi)/6, (7pi)/6, (11pi)/6\$

C) \$pi/6, (5pi)/6, (11pi)/6\$

D) \$pi/6, (5pi)/6, (7pi)/6, (11pi)/6\$