Question

prove that cosec to power 6 q= 3cot to power 6 q + 3cotq cosec to power 3 q+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