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Prove that cos^(-1).(4)/(5) + cos^(-1).(...

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

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`cos^(-1).(4)/(5) + cos^(-1).(12)/(13)`
`= tan^(-1).(3)/(4) + tan^(-1).(5)/(12) = tan^(-1). ((3)/(4) + (5)/(12))/(1 - ((3)/(4)) ((5)/(15))) ( :' (3)/(4) xx (5)/(12))`
`= tan^(-1) ((36 + 20)/(48 - 15)) = tan^(-1).(56)/(33)`
`= cos^(-1).(33)/(sqrt(33^(2) + 56^(2))) = cos^(-1).(33)/(65)`
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