Question

cosecX-cotX=1/√3 find cosx​

Answer 1

Answer:

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]

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Answer 2

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