How do you simplify $sin ({sin}^{- 1} (\frac{3}{5}) + {tan}^{- 1} (\frac{7}{24}))$ $sin(sin^-1( 3/5) + tan^-1( 7/24))$ ?

Question

How do you simplify $sin ({sin}^{- 1} (\frac{3}{5}) + {tan}^{- 1} (\frac{7}{24}))$ $sin(sin^-1( 3/5) + tan^-1( 7/24))$ ?

1 Answer

Impact of this question

4893 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-16T08:45:48

$= \frac{4}{5}$ $=4/5$

Explanation:

$= sin ({sin}^{-!} (\frac{3}{5}) + {cot}^{- 1} (\frac{24}{7}))$ $=sin(sin^-!(3/5)+cot^-1(24/7))$
$= sin ⎛ ⎝ {sin}^{-!} (\frac{3}{5}) + {csc}^{- 1} \sqrt{1 + {(\frac{24}{7})}^{2}} ⎞ ⎠$ $=sin(sin^-!(3/5)+csc^-1sqrt(1+(24/7)^2))$
$= sin ({sin}^{-!} (\frac{3}{5}) + {csc}^{- 1} (\frac{25}{7}))$ $=sin(sin^-!(3/5)+csc^-1(25/7))$
$= sin ({sin}^{-!} (\frac{3}{5}) + {sin}^{- 1} (\frac{7}{25}))$ $=sin(sin^-!(3/5)+sin^-1(7/25))$

$= {sin sin}^{-!} (\frac{3}{5}) {cos sin}^{- 1} (\frac{7}{25}) + {cos sin}^{-!} (\frac{3}{5}) {sin sin}^{- 1} (\frac{7}{25}))$ $=sinsin^-!(3/5)cossin^-1(7/25)+cossin^-!(3/5)sin sin^-1(7/25))$
$= (\frac{3}{5}) {cos cos}^{- 1} \sqrt{1 - {(\frac{7}{25})}^{2}} + cos s {cos}^{- 1} \sqrt{1 - {(\frac{3}{5})}^{2}} {sin sin}^{- 1} (\frac{7}{25})$ $=(3/5)coscos^-1sqrt(1-(7/25)^2)+cosscos^-1sqrt(1-(3/5)^2)sin sin^-1(7/25)$
$= \frac{3}{5} \times \frac{24}{25} + \frac{4}{5} \times \frac{7}{25} = \frac{100}{125} = \frac{4}{5}$ $=3/5xx24/25+4/5xx7/25=100/125=4/5$

Science

Math

Humanities

... and beyond

How do you simplify $sin ({sin}^{- 1} (\frac{3}{5}) + {tan}^{- 1} (\frac{7}{24}))$ $sin(sin^-1( 3/5) + tan^-1( 7/24))$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify sin(sin−1(35)+tan−1(724))sin(sin^-1( 3/5) + tan^-1( 7/24))?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify $sin ({sin}^{- 1} (\frac{3}{5}) + {tan}^{- 1} (\frac{7}{24}))$ $sin(sin^-1( 3/5) + tan^-1( 7/24))$ ?