मूल्यांकन कीजिए - `cos(2cos^(-1)x+sin^(-1)x), x=(1)/(5)," जहाँ "0le cos^(-1) x lepi" और "-(pi)/(2) le sin^(-1)x le (pi)/(2).`
मूल्यांकन कीजिए -
`cos(2cos^(-1)x+sin^(-1)x), x=(1)/(5)," जहाँ "0le cos^(-1) x lepi" और "-(pi)/(2) le sin^(-1)x le (pi)/(2).`
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`cos(2cos^(-1)x+sin^(-1)x)`
`=cos[cos^(-1)x+(cos^(-1)x+sin^(-1)x)]`
`=cos(cos^(-1)x+(pi)/(2))`
`=-sin(cos^(-1)x),`
`" "[because cos((pi)/(2)+theta)=-sin theta]`
`=-sin(sin^(-1)sqrt(1-x^(2))),`
`[because cos^(-1)x=sin^(-1)sqrt(1-x^(2))]`
`=-sqrt(1-x^(2))`
`x=(1)/(5) "पर ,"`
`cos(2cos^(-1)x+sin^(-1)x)=-sqrt(1-((1)/(5))^(2))`
`=-sqrt((24)/(25))`
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