Question

Find the value of tan (2 tan^-1 1/5)​

Answer 1

hello users ......

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we have to find:

the value of tan( 2 tan-¹ 1/5 ) = ?

solution:-

we know that:-

2tan -¹ x = tan-¹ {2x /(1-x²) }

here,

tan( 2 tan-¹ 1/5 )

= tan [ tan-¹ {2×1/5 / (1- 1²/5² ) } ]

=> tan [ tan-¹ 2/5 / (1-1/25) ]

=> tan [ tan-¹ (2/5 ) / (24/25) ]

=> tan [ tan-¹ 10/24 ]

=> tan[tan-¹ 5/12 ]

=> 5/12

..=> tan( 2 tan-¹ 1/5 ) = 5/12 Answer

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⭐✡ hope it helps ✡⭐