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AP EAMCET · Maths · Inverse Trigonometric Functions

If k=1ntan-11k2+k+1=tan-1θ, then θ=

  1. A nn+2
  2. B nn+1
  3. C 1
  4. D nn-1
Verified Solution

Answer & Solution

Correct Answer

(A) nn+2

Step-by-step Solution

Detailed explanation

It is given that, ∑k=1ntan-11k2+k+1=tan-1θ Simplifying the above expression we get, ∑k=1ntan-1(k+1)-k1+k(k+1)=tan-1θ ⇒∑k=1ntan-1(k+1)-tan-1k=tan-1θ tan-12-tan-11+tan-13-tan-12+tan-14-tan-13+…+tan-1(n+1)-tan-1n=tan-1θ…