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

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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