Find the Exact Value of the Given Expression $$\sin 105 ^ { \circ } \cos 345 ^ { \circ } - \sin 345 ^ { \circ } \cos 105 ^ { \circ }$$

question 47

Multiple Choice

Find the exact value of the given expression. $$\sin 105 ^ { \circ } \cos 345 ^ { \circ } - \sin 345 ^ { \circ } \cos 105 ^ { \circ }$$

• A) \(\frac { 1 } { 2 }\)
• B) \(\frac { ( - \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }\)
• C) \(\frac { ( - \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }\)
• D) \(\frac { \sqrt { 2 } } { 2 }\)
• E) \(\frac { \sqrt { 3 } } { 2 }\)

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Definitions:

Amniote

Vertebrate whose egg has waterproof membranes that allow the embryo to develop away from water; a reptile, bird, or mammal.

Amphibians

Cold-blooded vertebrates that typically begin life in water with gills and metamorphose, developing lungs to live both in water and on land.

Carnivores

Organisms that primarily eat meat, typically animals that have adaptations for hunting and consuming other organisms.

Fully Terrestrial

An organism or system that lives, operates, or performs its entire lifecycle on land with no aquatic phase.