Evaluate:sin(2cos−153).

Now,sin(2cos−153)=2sin(cos−153).cos(cos−153)=2sin⎝⎛sin−11−(53)2⎠⎞.cos(cos−153)=2.(1−259).53=2.54.53=2524.

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Evaluate: (2^{-1}{3}{5}).

Question

Evaluate:
$sin (2 cos^{- 1} \frac{3}{5})$ .

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Evaluate:

sin (2 cos^{- 1} \frac{3}{5})

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Now,

sin (2 cos^{- 1} \frac{3}{5})

= 2 sin (cos^{- 1} \frac{3}{5})

. cos (cos^{- 1} \frac{3}{5})

= 2 sin ⎝ ⎛ sin^{- 1} 1 - (\frac{3}{5})^{2} ⎠ ⎞

. cos (cos^{- 1} \frac{3}{5})

= 2. (1 - \frac{9}{25}) . \frac{3}{5}

= 2. \frac{4}{5} . \frac{3}{5}

= \frac{24}{25}

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