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Question
Evaluate: tan `[ 2 tan^-1 (1)/(2) – cot^-1 3]`
Solution
tan `[ 2 tan^-1 (1)/(2) - cot^-1 3]`
= tan `[tan^-1((2xx(1)/(2))/(1-(1/2)^2]) – cot^-1 3]`
= tan `[tan^-1{(1)/(1-(1)/(4)}} - tan^-1 1/3]`
= tan `[tan^-1 4/3 - tan^-1 (1)/(3)]`
= tan `[tan^-1 (((4)/(3) - (1)/(3))/(1+(4)/(9)))]`
= tan `[tan^-1 (((4 -1)/(3))/((9+4)/(9)))]`
= tan `[tan^-1 (1/(13/9))]`
= tan `[tan^-1 ((9)/(13)) ]`
= `(9)/(13)`
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