If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
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Solution
LHS = mn
`= (cosec theta + cot theta) (cosec theta - cot theta)`
`= cosece^2 theta - cot^2 theta`
= 1 [∵ `(1 + b)(a - b) = a^2 - b^2 cosec^2 theta - cot^2 theta = 1`]
=RHS
Concept: Trigonometric Identities
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