Simplify the expression
\$ ("cos"^4θ - "sin"^4θ )/( 10"sin"θ"cos"θ ) \$.

A) \$ (1/5) "cot"2θ\$

B) \$ (1/5)"cot"4θ\$

C) \$ (2/5)"cot"2θ\$

D) \$ (3/5) "cot"2θ\$

A ladder is leaning against a wall. If the foot of the ladder is 5 meters away from the wall and the ladder is 10 meters long, find the angle the ladder makes with the ground.

A) 30°

B) 60°

C) 90°

D) 45°

If \$ "sin"(α) = 4/5 \$ and sec(α) > 0, find cot(α).

A) \$ 5/2 \$

B) \$ 7/2 \$

C) \$ 3/4 \$

D) \$ 2/9 \$

Given that \$ "tan"(β) = 3/4 \$​, express sin(β) and cos(β) in terms of β using reciprocal identities, then evaluate \$ "sin"^2(β) + "cos"^2(β) \$.

A) 4

B) 2

C) 8

D) 1

Solve for cos(2α) given that \$ "sin"(α) = - 5/13 \$ and \$ "cos"(α) = 12/13 \$ (α is in Quadrant II).

A) \$ 119/139 \$

B) \$ 129/159 \$

C) \$ 109/169 \$

D) \$ 119/169 \$

Which of the following equations is a trigonometric identity?

A) \$("sin" "x") / (1 - "cos" "x") = ("csc" "x" - "cot" "x") \$

B) \$("sin" "x")(1 - "cos" "x") = ("csc" "x" + "cot" "x") \$

C) \$("sin" "x") / (1 - "cos" "x") = ("csc" "x" + "cot" "x")\$

D) \$("sin" "x") / (2 + "cos" "x") = ("csc" "x" - 2"cot" "x")\$

Simplify the expression
\$(2 "sin" "x" "sec"^3 "x")/(1 - "tan"^4 "x")\$.

A) cos2x

B) tan2x

C) cosx

D) tan3x

Verify the statement:
\$"csc"^4 \theta - "cot"^4 \theta = 2"csc"^2 \theta - 1\$.

A) \$"cot"^2\theta + 1 = "csc"^2\theta\$

B) \$"cot"^2\theta + 1 = "sec"^2\theta\$

C) \$"cos"^2\theta + 1 = "csc"^2\theta\$

D) \$"cot"^2\theta + 2 = "sec"^2\theta\$

\$((1 + "sin" "x")^2 + (1 - "sin" "x")^2)/(2 "cos"^2 "x")\$
What does the following expression simplify to after applying trigonometric identities?

A) \$("sin"^2 "x" + 1)/("sin"^2 "x")\$

B) \$("sin"^2 "x" + 1)/("cos"^2 "x")\$

C) \$("sin"^2 "x" + 1)("sin"^2 "x")\$

D) \$("cos"^2 "x" + 1)/("sin"^4 "x")\$

Verify the identity:
\$("tan" "x")/(1 - "cot" "x") + ("cot" "x")/(1 - "tan" "x") = 1 + "tan" "x" + "cot" "x"\$.

A) \$"LHS" > "RHS"\$

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

C) LHS = RHS

D) None of the above