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प्रश्न
Show that `tan^-1 1/2 = 1/3 tan^-1 11/2`
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उत्तर
We have to show that
`tan^-1 1/2 = 1/3 tan^-1 11/2`
i.e. to show that `3 tan^-1 1/2 = tan^-1 11/2`
LHS = `3 tan^-1 1/2`
`= 2 tan^-1 1/2 + tan^-1 1/2`
`= tan^-1 [(2 xx 1/2)/(1 - (1/2)^2)] + tan^-1 1/2 .....[∵ 2tan^-1 "x" = tan^-1 ("2x"/"1 - x"^2)]`
`= tan^-1 [1/(3/4)] + tan^-1 1/2`
`= tan^-1 4/3 + tan^-1 1/2`
`= tan^-1 [(4/3 + 1/2)/(1 - 4/3 xx 1/2)]`
`= tan^-1 ((8 + 3)/(6 - 4))`
`= tan^-1 (11/2)` = RHS
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