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Scosecx.log(cos ecx - cotx) dx =(1) logº (cos eex + cotx) +C(2) -- log? (cosecx - cotx)+Clog(3)log (cosecx - cotx)+C(4) --log(cos ecx - cotx)+C22 |
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Answer» 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. Step-by-step explanation: i hope help you |
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