Question

Find the value of tan-1(1) + tan-1(2)+ tan-1(3) = …?​

Answer 1

Answer:

Let  tan−1(1)=x

⇒1=tanx

Let  tan−1(2)=y

⇒2=tany

Let  tan−1(3)=z

⇒3=tanz

tan(x+y+z)=1−tanx.tany−tanx.tanz−tany.tanztanx+tany+tanz−tanx.tany.tanz

=1−1×2−1×3−2×31+2+3−1×2×3

=0

⇒x+y+z=π

 tan−1(1)+tan−1(2)+tan−1(3)=π

(  x+y+z  cannot be equal to zero, because

 tan−1(1)+tan−1(2)+tan−1(3) will have some value greater than zero )

Step-by-step explanation:

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