Maharashtra State BoardHSC Arts 12th Board Exam
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Prove that 2tan-1(34)=tan-1(247) - Mathematics and Statistics

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Sum

Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`

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Solution

`2 tan^-1 (3/4)`

= `tan^-1 (3/4) + tan^-1 (3/4)`

= `tan^-1 ((3/4 + 3/4)/(1 - 3/4 xx 3/4))`   .......`[tan^-1"a" + tan^-1"b" = tan^-1(("a" + "b")/(1 - "ab"))]`

= `tan^-1 ((6/4)/(7/16))`

= `tan^-1 (24/7)`

Concept: Inverse Trigonometric Functions
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