Q. 224.6( 9 Votes )

If cotx(1 + sinx) = 4m and cotx(1 – sinx) = 4n, prove that (m2 – n2)2 = mn.

Answer :

Given 4m = cotx (1+ sinx) and 4n = cotx (1 – sinx)


Multiplying both equations, we get


16mn = cot2x (1 – sin2x)


We know that 1 – sin2x = cos2x


16mn = cot2x cos2x


… (1)


Squaring the given equations and then subtracting,


16m2 = cot2x (1+ sinx)2 and 16n2 = cot2x (1 – sinx)2


16m2 – 16n2 = cot2x (4 sinx)



Squaring both sides,



… (2)


From (1) and (2),


(m2 – n2) = mn


Hence proved.


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