Question

soumon Let ( sin ^{-1} frac{3}{5}=x ) and ( sin ^{-1} frac{8}{17}=y . ) Then,
( sin x=frac{3}{5} ) and ( sin y=frac{8}{17} )
( therefore quad cos x=sqrt{1-sin ^{2} x}=sqrt{1-frac{9}{25}}=sqrt{frac{16}{25}}=frac{4}{5} )
[
begin{array}{l}
text { and } cos y=sqrt{1-sin ^{2} y}=sqrt{1-frac{64}{289}}=sqrt{frac{225}{289}}=frac{15}{17}
begin{aligned}
therefore quad cos (x-y)=cos x cos y+sin x sin y &=left(frac{4}{5} times frac{15}{17}right)+left(frac{3}{5} times frac{8}{17}right)=left(frac{12}{17}+frac{24}{85}right)=frac{84}{85}
{ }{=} & x-y=cos ^{-1}left(frac{84}{85}right) Rightarrow sin ^{-1} frac{3}{5}-sin ^{-1} frac{8}{17}=cos ^{-1} frac{84}{85}
end{aligned}
end{array}
]

# EXAMPLE 18 Prove that sin - 3 - sin , co-184

Solution