Given \$"sin" \theta = (\sqrt(3))/2\$ for \$90^\circ <\theta <180^\circ\$ find the value of \$"cos" \theta\$ using the pythagorean identity.

A) \$1/2\$

B) -2

C) \$-1/2\$

D) 2

Given that sin(x) = \$3/5\$ and cos(y) = \$7/25\$, find the exact value of
tan(x + y).

A) \$ - 171/44 \$

B) \$ - 113/28 \$

C) \$ - 111/28 \$

D) \$ - 117/44 \$

Simplify \$(("sin" \theta) / (1 + "cos" \theta)) + ((1 + "cos" \theta) / ("sin"\theta))\$ by using reciprocal trigonometric identity.

A) \$"csc" \theta\$

B) \$-"csc" \theta\$

C) \$-2 "csc"\theta\$

D) \$2"csc"\theta\$

Simplify the expression \$"tan" x("cosx" + "cot x")/("sec x" + "tan x")\$ using reciprocal identities.

A) - 1 + sinx

B) tan2x

C) cosx

D) cot2x

Simplify \$(("sin"^2\theta) /("cos"\theta)) + (("cos"^2\theta) /("sin"\theta))\$.

A) \$secθ - cosθ + cscθ - sinθ\$

B) \$cosθ + secθ + sinθ + cscθ\$

C) \$cosθ − secθ + sinθ − cscθ \$

D) \$secθ + cosθ − cscθ + sinθ\$