Simplify the expression:
\$ 1/(1 - "sin" "x" ) + 1/(1 + "sin" "x" ) \$.

A) \$2"sec"^2 ("x") \$

B) \$"csc"^2 ("x") \$

C) \$2"cos"^2 ("x") \$

D) \$2"sin"^2 ("x") \$

Verify the identity:
\$ ( 1 + "tan"θ )^2 = ( 1 + 2 "sin"θ "cos"θ)/("cos"^2 θ) \$.

A) 0

B) Proved

C) Not proved

D) 1

Simplify the expression:
\$ ("sin"^3 "x" - "sin" "x")/("cos" "x" - "cos"^3 "x") \$.

A) - tan x

B) - csc x

C) - cot x

D) - sec x

Simplify the following expression:
\$"tan"^2 ("x") ( 1 + "cot"^2 ("x"))\$.

A) \$"csc"^2 ("x") \$

B) \$"cot"^2 ("x") \$

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

D) \$"sec"^2 ("x")\$

Simplify the following expression: \$"tan"^2 θ - "sin"^2 θ\$.

A) \$- "tan"^2θ . "sin"^2θ\$

B) \$"tan"^2θ + "sin"^2θ\$

C) \$"tan"^2θ\$

D) \$"tan"^2θ . "sin"^2θ\$

Verify that the Pythagorean identity relating sine and cosine is true for \$θ = pi/4\$.

A) \$"sin"^2(π/4) − "cos"^2(π/4)\$

B) \$"sin"(π/4) + "cos"(π/4)\$

C) \$"sin"^2(π/4) + "cos"^2(π/4)\$

D) \$"sin"(π/4) ⋅ "cos"(π/4)\$

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

A) cotθ - tanθ

B) cosθ - sinθ

C) cotθ + tanθ

D) cosθ + sinθ

Prove the identity:
\$("cos" "x") / ("tanx") - "cscx" = - "sinx"\$.

A) Proved

B) 1

C) Not proved

D) -1

Simplify the following identity using the trigonometry identities:

\$("sin" θ + "cosec" θ)^2 + ("cos" θ + "sec" θ)^2\$.

A) \$7 - "tan"^2 θ - "cot"^2 θ\$

B) \$7 + "tan"^2 θ + "cot"^2 θ\$

C) \$- 7 + "tan"^2 θ - "cot"^2 θ\$

D) \$7 - "tan"^2 θ + "cot"^2 θ\$

Simplify the following equation:
\$"sec"((3pi)/2 - "x")\$.

A) cscx

B) - secx

C) - csc x

D) secx