If \$"sin"(α) = 3/5\$ and \$"cos"(β) = 12/13\$ find the value of tan(α + β).

A) \$56/33 \$

B) \$33/56\$

C) \$- 28/33\$

D) \$- 33/56\$

\$2"sin"^2 (x) - \sqrt3 "sin"("x") + 1 = 0\$ for 0 ≤ x ≤ 2π: Use the quadratic formula to solve for sin(x), then apply the unit circle and Pythagorean identity to find the values of x.

A) 14

B) \$2/3\$

C) No solutions

D) 0

Simplify the expression \$("cos"^2θ)/(1 - "sin"θ ) + 1/("cos"θ) \$.

A) 1 - sinθ - secθ

B) 1 - sinθ + secθ

C) 1 + sinθ + secθ

D) sinθ + secθ -1

Simplify the expression \$("sin"^2(-\theta) - "cos"^2(\theta)) / ("sin"(-\theta) - "cos"(-\theta))\$.

A) \$"csc"\theta + "sec"\theta\$

B) \$"cos"\theta + "sin"\theta\$

C) \$"csc"\theta - "sec"\theta\$

D) \$"cos"\theta - "sin"\theta\$

Prove \$("sin"(2x))/("sin"(x)) - ("cos"(2"x"))/("cos"("x")) = "sec"("x")\$.

A) Not proved

B) Infinity

C) 0

D) Proved

Prove the following identity: \$(("sin"^2\theta)/ ("csc"\theta) - ("sin"\theta)) + (("cos"^2\theta) / ("sec"\theta) - ("cos"\theta))\$ = \$1/("sin"\theta + "cos"\theta)\$.

A) Not proved

B) 0

C) Proved

D) Infinity

If sin θ and cos θ are the roots of the quadratic equation \$"x"^2 + "px" + 2 = 0\$, find p.

A) \$ \pm \sqrt3 \$

B) \$ \pm \sqrt5 \$

C) \$ \pm \sqrt2 \$

D) \$ \pm \sqrt7\$

cot(x) = \$7/24\$, find sin(x) using the reciprocal identity.

A) \$24/25\$

B) \$7/25\$

C) \$- 25/24\$

D) \$- 24/25\$

If \$"cos"(θ) = -1/2\$ and θ is in the third quadrant, find the values of sin(θ) and tan(θ).

A) \$"sin"\theta = \sqrt(3)/2\$ and \$"tan"\theta = -\sqrt(3)\$

B) \$"sin"\theta = -\sqrt(3)/2\$ and \$"tan"\theta = \sqrt(3)\$

C) \$"sin"\theta = \sqrt(3)/2\$ and \$"tan"\theta = \sqrt(3)\$

D) \$"sin"\theta = -\sqrt(3)/2\$ and \$"tan"\theta = -\sqrt(3)\$

Simplify the expression \$"tan"^2(x) - "sin"^2(x)\$.

A) \$-"tan"^2(x)"sin"^2(x)\$

B) \$"tan"^2(x) - "sin"^2(x)\$

C) \$"tan"^2(x)"sin"^2(x)\$

D) \$-"tan"^2(x) + "sin"^2(x)\$