If \$"cot" \theta = 3/4\$ and \$"sin"\theta\$ < 0, find \$"csc" \theta\$.

A) \$- 5/4\$

B) \$ 4/5 \$

C) \$ 3/4\$

D) \$- 4/3\$

Simplify the following expression \$ ("cot"^2("x")) / ("csc"("x") - "sin"("x"))\$.

A) - sec(x)

B) csc(x)

C) sin(x)

D) - cos(x)

Triangle PQR is a right triangle with a 90-degree angle at vertex Q. The length of side PQ is 25 and the length of side QR is 60. Triangle STU is similar to triangle PQR. The vertices S, T, and U correspond to vertices P, Q, and R, respectively. What is the value of cos∠U?

A) \$5/13\$

B) \$5/12\$

C) \$12/13\$

D) \$5/6\$

Simplify: \$"sin"^2(x)"tan"^2("x") + "cos"^2(x)\$.

A) \$csc^2(x)- 2cos^2(x)\$

B) \$sec^2(x) + tan^2(x)\$

C) \$csc^2(x) - cot^2(x)\$

D) \$sec^2(x) - 2sin^2(x)\$

Find the value of the expression using a reciprocal identity. \$"sin"\theta = -1/2\$ and \$"tan"\theta = \sqrt(3)/3\$, \$"cos"\theta\$.

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

B) \$- \sqrt(3)/2\$

C) \$-\sqrt(2)/3\$

D) \$\sqrt(3)/2\$

Simplify: \$ ("sin"(θ) + "cos"(θ))/("sin"(θ) − "cos"(θ)) \$.

A) \$ ( 1 + "sin"2θ)/("cos"2θ) \$

B) \$ ( 1 - "sin"2θ)/("cos"2θ) \$

C) \$ - (( 1 + "sin"2θ))/("cos"2θ) \$

D) \$ - ( (1 - "sin"2θ))/("cos"2θ) \$

\$"csc"\theta = ((2\sqrt(3))/3)\$, find \$"sin"\theta\$ using the reciprocal identity.

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

B) \$\sqrt(3)/2\$

C) \$- 2/\sqrt(3)\$

D) \$- 2/\sqrt(2)\$

Given that sin(α) = \$3/5\$ and cos(β) = \$4/5 \$ find the exact value of
cos (α - β).

A) 1

B) \$8/5\$

C) 0

D) \$19/21\$

Simplify \$ ("sec"("x")"sin"^2("x"))/(1 + "sec"("x")) \$.

A) 1 + cosx

B) - cos(x) + 1

C) 1 - sinx

D) tan(3x) + 1

Simplify \$("cscx" + "cotx") (( 1 - "cosx")/("sinx") ) \$.

A) \$ 1/("sinx") \$

B) \$ ("sinx")/("cosx") \$

C) 1

D) \$ 1/"cosx"\$