1.

Prove that 2 tan^(-1)(1/2) + tan^(-1)(1/7) = tan^(-1)(31/17)

Answer»

SOLUTION :
L.H.S =`TAN^(-1)((2xx1/2)/(1-(1/2)^2)) + tan^(-1)(1/7)`
`= tan(1/(1-1/4)) + tan^(-1)(1/7) = tan^(-1)(4/3) + tan(1/7)`
` - tan^(-1)((4/3 + 1/7)/(1-4/3xx1/7)) = tan^(-1)((31/21)/(17/21)) - tan^(-1) (31/17)` = R.H.S


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