# If (cosec θ + cot θ) = m and (cosec θ – cot θ) = n, show that mn = 1

Given: (cosec θ + cot θ) = m …………….(1)

(cosec θ – cot θ) = n …………….(2)

Multiply equation (1) and (2):

(cosec θ + cot θ) (cosec θ – cot θ) = mn

(cosec2 θ – cot2 θ) = mn

1 = mn ( 1 + cot2 θ = cosec2 θ)

Therefore, mn = 1.

Hence, proved.

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