Question

2 sin inverse 4/5 + sin inverse 24/25​

Answer 1

$sin^{-1}$(x)+$sin^{-1}$(y)=$sin^{-1}$[$\sqrt{1-y^{2} }$+y$\sqrt{1-x^{2} }$ ]

x=4/5

and y=24/25

$sin^{-1}\frac{4}{5} +(sin^{-1}\frac{4}{5}$+$sin^{-1}\frac{24}{25})$

$sin^{-1} [\frac{4}{5}\sqrt{1-\frac{24}{25} ^{2}}+\frac{24}{25}\sqrt{1-\frac{4}{5} ^{2} ]$=$(sin^{-1}\frac{4}{5}$+$sin^{-1}\frac{24}{25})$

$sin^{-1} [\frac{4}{5}\sqrt{1-\frac{576}{625} }+\frac{24}{25}\sqrt{1-\frac{16}{25} ]$

$sin^{-1} [\frac{4}{5}\sqrt{\frac{49}{625} }+\frac{24}{25}\sqrt{\frac{9}{25} ]$

$sin^{-1} [\frac{4}{5}(\frac{7}{25})+\frac{24}{25}(\frac{3}{5} ) ]$

$sin^{-1} [\frac{28}{125}+\frac{72}{125} ]$

$sin^{-1} [\frac{100}{125}]$

$sin^{-1} [\frac{4}{5}]$=$(sin^{-1}\frac{4}{5}$+$sin^{-1}\frac{24}{25})$

$(sin^{-1}\frac{4}{5}$+$sin^{-1}\frac{4}{5})$

$sin^{-1} [\frac{4}{5}\sqrt{1-\frac{4}{5} ^{2}}+\frac{4}{5}\sqrt{1-\frac{4}{5} ^{2} ]$

$sin^{-1} [\frac{4}{5}(\frac{3}{5} )+\frac{4}{5}(\frac{3}{5}) ]$

$sin^{-1} [\frac{12}{25} +\frac{12}{25} ]$

$sin^{-1}\frac{24}{25}$