If two angles of a triangle are `tan^(-1) (2) and tan^(-1) (3)`, then find the third angles

If two angles of a triangle are `tan^(-1) (2) and tan^(-1) (3)`, then

1.	If two angles of a triangle are `tan^(-1) (2) and tan^(-1) (3)`, then find the third angles
Answer» Given two angles are `tan^(-1) (2) and tan^(-1) (3)`. Now `(2) (3) gt 1` `rArr tan^(-1) (2) and tan^(-1) (3) = pi + tan^(-1) ((2+3)/(1 - 2 xx 3))` `= pi + tan^(-1) = pi - (pi)/(4) = (3pi)/(4)` Hence, the third angle is `pi - (3pi)/(4) = (pi)/(4)`

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