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in Sets, relations and functions by (54.5k points)

If p > q > 0, pr < - 1 < qr, then prove that tan-1((p - q)/(1 + pq)) + tan-1((q - r)/(1 + qr)) + tan-1((r - p)/(1 + rp)) = π

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Best answer

We have

tan-1((p - q)/(1 + pq)) + tan-1((q - r)/(1 + qr)) + tan-1((r - p)/(1 + rp)) = π

= (tan-1p - tan-1q) + (tan-1q - tan-1r) + p + (tan-1r - tan-1p)

π

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