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Show that: 2 sin^-1 (3/5)-tan^-1 (17/31)=π/4 - Mathematics

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Show that:

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

 

 
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Solution

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

L.H.S 

`=cos^-1 (1-2 xx9/25)-tan^-1(17/31)`

`=cos^-1 (7/25) - tan^-1 (17/31)`

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

`=tan^-1 ((24/7-17/31)/(1+42/7xx17/31))`

`=tan^-1((24xx31-17xx7)/(31xx7+24xx17))`

`=tan^-1 (625/625)`

`=tan^(-1) 1`

`=pi/4`

Hence Proved

Concept: Inverse Trigonometric Functions (Simplification and Examples)
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