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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Prove the following: tan-1(12)+tan-1(13)=π4 - Mathematics and Statistics

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प्रश्न

Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`

बेरीज
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उत्तर

L.H.S. = `tan^-1(1/2) + tan^-1(1/3)`

= `tan^-1 [(1/2 + 1/3)/(1 - 1/2 * 1/3)]`    ...since `1/2 > 0, 1/3 > 0` and `(1/2)(1/3) < 1`

= `tan ^-1 ((5/6)/(1 - 1/6))`

= `tan^-1((5/6)/(5/6))`

= tan-1(1)

= `tan^-1(tan  pi/4)`

= `pi/(4)`

= R.H.S.

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पाठ 3: Trigonometric Functions - Exercise 3.3 [पृष्ठ १०३]
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