Question

If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1

Answer 1

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