cosec-¹(1/4cos³2x-3cos2x)
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Step-by-step explanation:
SOLUTION
Let y = cosec
cosec-1(14cos32x-3cos2x)
= cosec
cosec-1(1cos6x) ...[∵ cos3x = 4cos3x – 3cosx]
= cosec–1(sec6x)
= coseccosec
cosec-1[cosec(π2-6x)]
=
π2-6x
Differentiating w.r.t. x, we get
dy
dx
d
dx
dydx=ddx(π2-6x)
=
d
dx
d
dx
ddx(π2)-6ddx(x)
= 0 – 6 x 1
= –6.
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