Question

Prove the following trigonometric identities. $cot^{2}Acosec ^{2}B-cot^{2}Bcosec^{2}A=cot^{2}A-cot^{2}B$

Answer 1

Answer with Step-by-step explanation:

Given :  

cot²Acosec²B – cot²Bcosec²A = cot²A – cot²B

LHS : cot²Acosec²B – cot²Bcosec²A

= cot²A(1 + cot²B) − cot²B(1 + cot²A)

[By using  an identity, cosec²θ = (1+ cot²θ) ]

= cot²A +  cot²Acot²B − cot²B -  cot²Acot²B

= cot²A − cot²B +  cot²Acot²B -  cot²Acot²B

= cot²A − cot²B

cot²Acosec²B – cot²Bcosec²A = cot²A – cot²B

L.H.S = R.H.S  

Hence Proved..

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

Hey mate plzz refer to the attachment