Question

Cosec6=cot6+3cot2cosec2+1

Answer 1

Answers

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 IT HELPS..!!

GOOD LUCK FOR FUTURE..!!

Answer 2

Answer:

(1+ cot^2)^3

(1)^3 + cot^6 + 3cot^2(1+cot^2)

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