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Question
Prove that: `cos^-1 4/5+cos^-1 12/13=cos^-1 33/65`
Solution
LHS = `cos^-1 4/5+cos^-1 12/13`
`=cos^-1[4/5xx12/13-sqrt(1-(4/5)^2)sqrt(1-(12/13)^2)]` `[becausecos^-1x+cos^-1y=cos^-1(xy-sqrt(1-x^2)sqrt(1-y^2)]`
`=cos^-1[48/65-3/5xx5/13]`
`=cos^-1((48-15)/65)`
`=cos^-1 33/65=` RHS
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