Question

cosec⁶ theta = cot⁶ theta + 3cot² theta.cosec² theta +1​

Answer 1

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