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Prove that : 2 Sin − 1 ( 3 5 ) − Tan − 1 ( 17 31 ) = π 4 . - Mathematics

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Sum

Prove that : `2sin^-1 (3/5) -tan^-1 (17/31) = pi/4.`

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Solution

LHS: `2sin^-1  ((3)/(5))-tan^-1  ((17)/(31))`

 

`= 2tan^-1(3/4) - tan^-1(17/31)`

 

= `tan^-1  ((6/(4))/(1-9/16)) - tan^-1  (17)/(31)`


⇒ = `tan^-1  (24)/(7) - tan^-1  (17)/(31)`


 = `tan^-1  ((24/7 - 17/34)/(1+ 24/7 xx 17/31))`


= `tan^-1  ((625)/625)`


= `tan^-1 (1)`


= `pi/(4) = "RHS"`.

Concept: Proof Derivative X^n Sin Cos Tan
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