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Question
Prove the following result
`cos(sin^-1 3/5+cot^-1 3/2)=6/(5sqrt13)`
Solution
LHS = `cos(sin^-1 3/5+cot^-1 3/2)`
`=cos(sin^-1 3/5+tan^-1 2/3)`
`=cos[cos^-1sqrt(1-(3/5)^2)+cos^-1 1/sqrt(1+(2/3)^2)]`
`=cos(cos^-1 4/5+cos^-1 3/sqrt13)`
`=cos{cos^-1[4/5xx3/sqrt13-sqrt(1-(4/5)^2)sqrt(1-(3/sqrt13)^2]}`
`=cos{cos^-1[12/(5sqrt13)-6/(5sqrt13)]}`
`=cos{cos^-1[6/(5sqrt13)]}`
`=6/(5sqrt13)=`RHS
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