CBSE

MATHEMATICS · Multi-part · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Let x>0x>0. (i) Prove that arctan⁡x+arctan⁡(1x)=π2\arctan x+\arctan\left(\dfrac{1}{x}\right)=\dfrac{\pi}{2}. (ii) Using the result of part (i), evaluate S=arctan⁡2+arctan⁡12+arctan⁡3+arctan⁡13.S=\arctan 2+\arctan\dfrac{1}{2}+\arctan 3+\arctan\dfrac{1}{3}.

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