Math, asked by tejasshuklaa, 1 month ago

19. tan-¹ (a-b 1+ ab) + tan-¹ (b-c 1 + bc) is equal to​

Answers

Answered by piyushraj77391
1

Answer:

Let us assume that a=tanα, b=tanβ and c=tanγ

∴tan

−1

(

1+ab

a−b

)=tan

−1

(

1+tanαtanβ

tanα−tanβ

)

=tan

−1

(tan(α−β))

=α−β

Similarly, tan

−1

(

1+bc

b−c

)=β−γ and tan

−1

(

1+ac

c−a

)=γ−α

∴tan

−1

(

1+ab

a−b

)+tan

−1

(

1+bc

b−c

)+tan

−1

(

1+ac

c−a

)=α−β+β−γ+γ−α=

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