Question

cosec^6= cot^6+ 3 cot^2 cosec ^2 +1

Answer 1

 cosec 6A = cot 6A + 3 cot 2A cosec 2A + 1

Then, we will prove it as :

To Prove:

   cosec 6A = cot 6A + 3 cot 2A cosec 2A + 1

i.e.  cosec 6A – cot 6A – 3 cot 2A cosec 2A = 1

Taking L.H.S. ,

 cosec 6A – cot 6A – 3 cot 2A cosec 2A

= (cosec 2A)3 – (cot 2A)3 – 3 cot 2A cosec2A

= {(cosec 2A – cot 2A) ((cosec 2A)2 + (cot 2A)2 + cosec 2A cot 2A)}

= {1 ((cosec 2A)2 + (cot 2A)2 – 2 cosec 2A  cot 2A + 2 cosec 2A cot 2A + cosec 2A cot 2A)}  – 3 cot 2A cosec 2A

= {(cosec 2A – cot 2A)2 + 3 cosec 2A cot 2A}  – 3 cosec 2A cot 2A

= (cosec 2A – cot 2A)2

= (1)2

=  1

Hence,

   cosec 2A – cot 6A – 3 cot 2A cosec 2A = 1

⇒   cosec 2A = cot 6A + 3 cot 2A cosec 2A + 1


hope answer helpful

Answer 2

Heya mate!!

Your solution is in the attachment.

#Kevin

Hope it helps you :))

try to mark it as brainliest..