If tan^-1 1/1+1 2 + tan^-1 1/1+2 3 + tan^-1 1/1+n(n+1) - Maths - Inverse Trigonometric Functions

Question

If tan^-1 1/1+1 2 + tan^-1 1/1+2 3 + tan^-1 1/1+n(n+1) = tan^-1
theta
then find the value of theta

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

tan-111+1 2+tan-111+2 3+ +tan-111+nn+1=tan-1θtan-12-11+1
2+tan-13-21+2 3+
+tan-1n+1-n1+nn+1=tan-1θtan-12 - tan-11+tan-13-tan-12+
+tan-1n+1-tan-1n=tan-1θtan-1n+1-tan-11=tan-1θtan-1n+1-11+n+1=tan-1θ⇒θ=tan tan-1n+1-11+n+1⇒θ=n2+n   ANS
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If tan^-1 1/1+1.2 + tan^-1 1/1+2.3 + ........ tan^-1 1/1+n(n+1) = tan^-1 theta then find the value of theta.

If tan^-1 1/1+1.2 + tan^-1 1/1+2.3 + ........ tan^-1 1/1+n(n+1) = tan^-1 theta
then find the value of theta.