Find the Exact Value of the Expression $\cos \left[ \sin ^ { - 1 } \frac { 2 } { 3 } + 2 \sin ^ { - 1 } \left( - \frac { 1 } { 3 } \right) \right]$

question 273

Multiple Choice

Find the exact value of the expression.884:890
- $\cos \left[ \sin ^ { - 1 } \frac { 2 } { 3 } + 2 \sin ^ { - 1 } \left( - \frac { 1 } { 3 } \right) \right]$

• A) \(\frac { 2 \sqrt { 6 } } { 5 }\)
• B) \(\frac { 2 \sqrt { 3 } } { 5 }\)
• C) \(\frac { 2 \sqrt { 3 } + 2 \sqrt { 10 } } { 9 }\)
• D) \(\frac { 7 \sqrt { 5 } + 8 \sqrt { 2 } } { 27 }\)

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Definitions:

Club Fungi

A group of fungi characterized by the production of spores on club-shaped structures called basidia.

Fruiting Body

The reproductive structure produced by certain fungi and plants, designed for spore dissemination.

Mushroom

A type of fungus characterized by a cap on a stem, producing spores beneath the cap, and known for a variety of shapes, sizes, and colors.

Extracellular Digestion

The breakdown of food outside cells, typically seen in simple organisms or in certain animal digestive systems.