cosec⁶ theta = cot⁶ theta + 3cot² theta.cosec² theta +1
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Step-by-step explanation:
cosec
6
θ=(cosec
2
θ)
3
.
cosec
2
θ=cot
2
θ+1−−−−(1)
(cosec
2
θ)
3
=(cot
2
θ+1)
3
Since (x+y)
3
=x
3
+y
3
+3xy(x+y),we have
cosec
6
θ=(cot
2
θ)
3
+(1)
3
(cot
2
θ)(1)(cot
2
θ+1)
⇒cosec
6
θ=cot
6
θ+1+3.cot
2
.cosec
2
θ
⇒cosec
6
θ=cot
6
θ+3.cot
2
cosec
2
θ+1
∴ L.H.S=R.H.S
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