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

11th - 12th Class
Maths
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3
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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} ]
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