Q. 54.3( 9 Votes )

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

Answer :

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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