Find the value of sin cosa tano
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Find the value of sin cosa tano

11th - 12th Class
Maths
Solution
52
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( sin left[cos ^{-1} frac{4}{5}+tan ^{-1} frac{2}{3}right] ) ( operatorname{let} cos ^{-1} frac{4}{5}=0 ) ( Rightarrow frac{4}{5}=cos theta=frac{b}{h} ) ( p=sqrt{n^{2}-b^{2}} ) ( quad tan theta=frac{3}{4} Rightarrow theta=tan ^{2}-4^{2}=3 ) ( sin left[theta+tan ^{2}left(frac{2}{3}right)right] ) ( sin left[tan ^{-1}left(frac{3}{4}right)+tan ^{-1}left(frac{2}{3}right)right] ) ( sin left[tan ^{-1}left(frac{frac{3}{4}+frac{2}{3}}{1-frac{3}{4}, frac{2}{x}}right)right. ) ( sin tan ^{-1}left(frac{17}{20} times 4right) ) in tom ( ^{-1}left(frac{1}{a}right) ) let ( tan ^{-1} frac{17}{6}=2 ) ( begin{aligned} Rightarrow frac{17}{6}=tan 2=frac{p}{b} h &=sqrt{frac{117,2+612}{sqrt{289+36}}} &=sqrt{325} sin 2 &=frac{17}{sqrt{325}} sin 2 & frac{17}{325} Rightarrow z=sin frac{177}{sqrt{325}} end{aligned} ) Put ( (1), z=sin ^{-1} frac{17}{sqrt{25}} ) ( sin z ) ( =sin sin ^{-1} frac{17}{sqrt{325}}=frac{17}{sqrt{325}} d )
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