Question

Prove the following relations: cos²A + cos²A cot²A = cot²A
please help)):​

Answer 1

the function is an identity

Answer 2

see explanation

Explanation:

Using the identities

1 + cot²x = cosec²x

cosec²x =
`(1)/(sin^2x)` , cotx =
`(cosx)/(sinx)`

Consider the left side

cos²A + cos²A cot²A ← factor out cos²A from each term

= cos²A(1 + cot²A)

= cos²A × cosec²A

= cos²A ×
`(1)/(sin^2A)`

=
`(cos^2A)/(sin^2A)`

= cot²A

= right side , thus proven