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The Brainliest Answer!
2015-08-07T21:05:47+05:30
Given that

cosec x +cot x = k  --------------(1)
we know that 
cosec^2 x -cot^2 x = 1
(cosec x +cot x)(cosec x -cot x) = 1
k (cosec x-cot x) = 1
(cosec x-cot x) = 1/k  ------------------(2)

from (1) & (2)
cosec x+cot x = k
cosec x-cot x = 1/k

2cosec x = k+1/k
2cosec x= k^2+1/k
cosec x = k^2+1/2k
sin x = 2k/k^2+1
we know that 
cos x = √1-sin^2 x
cos x = √1-[2k/k^2+1]^2
cos x = √1-4k^2/(k^2+1)^2
cos x = √(k^2+1)^2-4k^2/(k^2+1)^2
cos x = √(k^2-1)^2/(k^2+1)^2                         {·(a+b)^2-(a-b)^2 = 4ab}
cos x = √[k^2-1/k^2+1]^2 
cos x = k^2-1/k^2+1

hence proved
2 4 2
want some easy answer
this is the answer
no other easy ways