What is $sin (arcsin (\frac{3}{5}) + (arctan - 2))$ $Sin(arcsin(3/5)+(arctan-2))$ ?

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What is $sin (arcsin (\frac{3}{5}) + (arctan - 2))$ $Sin(arcsin(3/5)+(arctan-2))$ ?

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Answer 1 · 2018-08-04T16:17:09

$- \frac{1}{\sqrt{5}}$ $- 1/sqrt 5$

Explanation:

$sin (arcsin (\frac{3}{5}) + arctan (- 2))$ $sin ( arcsin ( 3/5 ) + arctan ( - 2 ) )$

$= sin (arcsin (\frac{3}{5}) + arcsin (- \frac{2}{\sqrt{5}}))$ $= sin ( arcsin ( 3/5 ) + arcsin ( -2/sqrt5 ) )$

$= (sin arcsin (\frac{3}{5})) (cos arcsin (- \frac{2}{\sqrt{5}}))$ $= (sin arcsin (3/5)) (cos arcsin(-2/sqrt5))$

$+ (cos arcsin (\frac{3}{5})) (sin arcsin (- \frac{2}{\sqrt{5}}))$ $+ (cos arcsin (3/5))( sin arcsin(-2/sqrt5))$

$= \frac{3}{5} cos arccos (\frac{1}{\sqrt{5}}) + cos arccos (\frac{4}{5}) (- \frac{2}{\sqrt{5}})$ $= 3/5 cos arccos ( 1/sqrt5 ) + cos arccos ( 4/5) ( -2/sqrt5)$

$= (\frac{3}{5}) (\frac{1}{\sqrt{5}}) - (\frac{4}{5}) (\frac{2}{\sqrt{5}})$ $= (3/5)( 1/sqrt5 ) - ( 4/5 ) ( 2/sqrt5 )$

#= - 1/sqrt5

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What is $sin (arcsin (\frac{3}{5}) + (arctan - 2))$ $Sin(arcsin(3/5)+(arctan-2))$ ?

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