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Prove that: tan^(-1)4/5+cos^(-1)(12)/(13...

Prove that: `tan^(-1)4/5+cos^(-1)(12)/(13)=cos^(-1)(33)/(65)`

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Verified by Experts

`cos^(-1).(4)/(5)+cos^(-1).(12)/(13)=cos^(-1).(33)/(65)`
`because " "cos^(-1)x+cos^(-1)y=cos^(-1)(xy-sqrt(1-x^(2)sqrt(1-y^(2))))`
Taking L. H. S.,
`cos^(-1).(4)/(5)+cos^(-1).(12)/(13)`
`=cos^(-1)((4)/(5)xx(12)/(13)-sqrt(1-(16)/(25)sqrt(1-(144)/(169))))`
`=cos^(-1)((48)/(65)-sqrt((9)/(25))xxsqrt((25)/(169)))`
`=cos^(-1)((48)/(65)-(15)/(65))`
`=cos^(-1)((33)/(65))=R.H.S.`
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GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2014-SECTION-II
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