cosec theta- cot thetaa +1)(cosc theta + cot theta -1))
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Step-by-step explanation:
(Cosecθ - cotθ +1 )(cosecθ + cotθ -1)
=> [Cosecθ +(1 - Cotθ)][Cosecθ - ( 1- Cotθ)]
=> (Cosecθ)² - (1 - Cotθ)² (∵ (a + b)(a-b) = a² - b²)
=> Cosec²θ - (1 + Cot²θ - 2Cotθ) (∵ (a - b)² = a² + b² - 2ab)
=> Cosec²θ - 1 - Cot²θ + 2Cotθ
=> Cot²θ - Cot²θ + 2Cotθ (∵Cosec²θ - 1 = Cot²θ)
=> 2Cotθ.
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