InterviewSolution
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InterviewSolution
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`cos(sin^(-1).(3)/(5)+sin^(-1).(5)/(13))` का मान है - |
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Answer» माना `sin^(-1).(3)/(5)=A` और `sin^(-1).(5)/(13)=B,` जहाँ `A,B in [-(pi)/(2),(pi)/(2)]` तब `sinA=(3)/(5)` और `sinB=(5)/(13).` चूँकि `A, B in [-(pi)/(2),(pi)/(2)]` इसलिए `cosA, cosB gt 0` `therefore" "cosA=sqrt(1-sin^(2)A)` `=sqrt(1-(9)/(25))=(4)/(5)` `cosB=sqrt(1-sin^(2)B)` `=sqrt(1-(25)/(169))=(12)/(13).` अब, `cos(sin^(-1).(3)/(5)+sin^(-1).(5)/(13))=cos(A+B)` `=cosAcos B-sinAsinB` `=((4)/(5)xx(12)/(13))-((3)/(5)xx(5)/(13))` `=(48)/(65)-(15)/(65)` `=(33)/(65)`. |
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