if cot x equal to minus 3 by 5 x in 2 quadrant then find sinx by 2 cos x by 2 tan x by2
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Step-by-step explanation:
MATHS
If cosecx−cotx=
2
3
, Find cosx In which quadrant does x lie ?
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ANSWER
Given,
cosecx−cotx=
2
3
……. (1)
We know that , cosec
2
x−cot
2
x=
2
3
(cosecx+cotx)(cosecx−cotx)=1 …..(2)
From equation (1) and(2),
(cosec x+cotx)
2
3
=1
cosec x+cotx=
3
2
Add equation (1) to (3) we get,
2cosecx=
3
2
+
2
3
cosec x=
12
13
sinx=
13
12
sinx is positive it means “sinx ” lie in either first or second quadrant
Putting cosec x=
12
13
in equation (3) we get
cosec x+cotx=
3
2
12
13
+cotx=
3
2
cot x=−
12
5
cotx is negative so can either be in second or fourth quadrant
but sinx is also positive x must lie in second quadrant
Now cotx=
sinx
cosx
cosx=cotx×sinx
cosx=−
12
5
×
13
12
cosx=−
12
5
Hence x lie in second quadrant.
