দেওয়া আছে, A = (cotθ + cosecθ - 1) / (cotθ - cosecθ + 1) এবং B = cotθ + cosecθ। সমীকরণ (i) নং হতে পাই, A = (cotθ + cosecθ - (cosec²θ - cot²θ)) / (cotθ - cosecθ + 1) [∵ cosec²θ - cot²θ = 1] = ((cotθ + cosecθ) - (cosecθ + cotθ)(cosecθ - cotθ)) / (cotθ - cosecθ + 1) = ((cotθ + cosecθ)(1 - cosecθ + cotθ)) / (1 - cosecθ + cotθ) = cotθ + cosecθ = B। সুতরাং A² - B² = B² - B² = 0