Question

cosecx-cotx=1/2 0 <x <pie÷2 then cosx=?
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Answer 1

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As we know the trigonometric identity,

cosec2x−cot2x=1Or

(cosec x−cotx)(cosec x+cotx)=1

[As we know that

a2−b2=(a−b)(a+b)]

Here it is given that

cosec x −cotx = 12.....(1) , now putting this in above equation we get,

(cosec x−cotx)(cosec x+cotx)=1 1/2(cosec x+cotx)=1

cosec x+cotx=2........(2)now adding equation (1) and (2) we get,

2cosec x = 2+1/2=5/2or

cosec x = 5/2×2=5/4

So sin x = 1

cosec x=45

Now as we know that , cos x = 1−sin2x−−−−−−−−√=1−(4/5)2−−−−−−−√=25−16/25−−−−−√=9/25−−√=3/5[ Here only positive value will be considered because all other trigonometric ratios are in first quadrant]