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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Prove that 2tan-1(34)=tan-1(247) - Mathematics and Statistics

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प्रश्न

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

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उत्तर

`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)`

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पाठ 1.3: Trigonometric Functions - Very Short Answers
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