$2 \tan^{-1} \frac{1}{3} + \tan^{-1} \frac{1}{7} = ?$

দেওয়া আছে,
2tan^-1(1/3) + tan^-1(1/7)

আমরা জানি, 2tan^-1x = tan^-1[2x / (1 - x²)]
তাহলে, 2tan^-1(1/3) = tan^-1[2(1/3) / (1 - (1/3)²)]
= tan^-1[(2/3) / (1 - 1/9)]
= tan^-1[(2/3) / (8/9)]
= tan^-1[(2/3) × (9/8)]
= tan^-1(3/4)

এখন প্রদত্ত রাশিটি দাঁড়ায়:
tan^-1(3/4) + tan^-1(1/7)
আমরা জানি, tan^-1x + tan^-1y = tan^-1[(x + y) / (1 - xy)]
= tan^-1[(3/4 + 1/7) / (1 - (3/4 × 1/7))]
= tan^-1[((21 + 4)/28) / (1 - 3/28)]
= tan^-1[(25/28) / ((28 - 3)/28)]
= tan^-1[(25/28) / (25/28)]
= tan^-1(1)
= π/4