If (sec A + tan A - 1) (sec A - tan A + 1) = 3 tan A Which of the following is correct?

A) \$"LHS" ne "RHS"\$

B) \$"LHS" = "RHS"\$

C) LHS = 0

D) None of the above

Use reciprocal identities to simplify
\$ ("sec"^2 ("y") - "tan"^2 ("y"))/("sec"^2 ("y") + "tan"^2 ("y")) \$.

A) \$("cos"^2("y"))/(2 - "sin"^2("y"))\$

B) \$("cos"^2("y"))/(2 - "cos"^2("y"))\$

C) \$("sin"^2("y"))/(2 - "cos"^2("y"))\$

D) \$("sin"^2("y"))/(2 - "sin"^2("y"))\$

(1 + cos α)(1 + cos β)(1 + cos γ) = (1 – cos α)(1 – cos β)(1 – cos γ) What are the possible values for each member of the equation?

A) \$1 + "cos"^2(β)"cos"^2(γ)\$

B) \$"cos" α + "cos" β + "cos" γ \$

C) \$"sin" α "sin" β "sin" γ \$

D) 0

Which of the following trigonometric identities is correct?

A) \$(1/("sec"^2 "x" - "cos"^2 "x")) + ((1)/("cosec"^2 "x" - "sin"^2 x))"sin"^2 "x" . "cos"^2 "x" = ((2 - "sin"^2 "x" "cos"^2 "x")/(1 + "sin"^2 "x" "cos"^2 "x"))\$

B) \$(1/("sec"^2 "x" - "cos"^2 "x")) + ((1)/("cosec"^2 "x" - "sin"^2 "x"))"sin"^2 "x" . "cos"^2 "x" = ((1 - "sin"^4 "x" "cos"^4 "x")/(2 + "sin"^4 "x" "cos"^4 "x"))\$

C) \$(1/("sec"^2 "x" - "cos"^2 "x")) + ((1)/("cosec"^2 "x" - "sin"^2 "x"))"sin"^2 "x" . "cos"^2 "x" = ((1 - "sin"^4 "x" "cos"^4 "x")/(1 + "sin"^4 "x" "cos"^4 "x"))\$

D) \$(1/("sec"^2 "x" - "cos"^2 "x")) + ((1)/("cosec"^2 "x" - "sin"^2 "x"))"sin"^2 "x" . "cos"^2 "x" = ((1 - "sin"^2 "x" "cos"^2 "x")/(2 + "sin"^2 "x" "cos"^2 "x"))\$

Prove the identity: sin(2x)sin(3x)sin(5y) = \$(1/4) "sin"(10"x") − "sin"(8"x") − "sin"(6"x") + "sin"(4"x")\$.

A) LHS = 0

B) \$"LHS" > "RHS"\$

C) \$"LHS" = "RHS"\$

D) \$"LHS" ne "RHS"\$

Given that csc(β) = 2 and sec(β) = 3​, find the values of sin(2β) and cos(2β) using reciprocal identities.

A) \$ (1/6), (- 4/39)\$

B) \$ (1/5), (- 5/36)\$

C) \$ (1/3), (- 5/36)\$

D) \$ (1/3), (- 1/36)\$

Given the Pythagorean Identity: \$ "sin"^2("x") + "cos"^2("x") = 1 \$, prove the Double Angle Identity for Cosine: \$ "cos"(2"x") = "cos"^2("x") − "sin"^2("x") \$.

A) Not Proved

B) Proved

C) Inconclusive

D) Infinity

"Simplify the following expression:

\$ ("cot"^2(θ) - "csc"^2(θ))/ (1 + "cot"(θ)"tan"(θ)) \$

A) \$ -1/2 \$

B) \$ 4/3 \$

C) \$ 2/3 \$

D) \$ 1/2 \$

Solve the equation:
\$ "tan"^2(θ) + "sec"^2(θ) = 10 \$.

A) \$ (3sqrt2)/4 \$

B) \$ (3sqrt2)/2 \$

C) \$ (9sqrt4)/4 \$

D) \$ (5sqrt3)/3 \$

Prove the identity:
\$ "cos"(α)"sin"(β) = (1/2)("sin"(α + β) - "sin"(α - β)) \$

A) Not Proved

B) Infinity

C) Proved

D) Inconclusive