Question

Tan^2A -sin^2A=sin^2a Tan^2A​

Answer 1

see explanation

Explanation:

Using the identity

sin²A = 1 - cos²A , tanA =
`(sinA)/(cosA)`

Consider the left side

tan²A - sin²A

=
`(sin^2A)/(cos^2A)` - sin²A

`(sin^2A-sin^2Acos^2A)/(cos^2A)`

=
`(sin^2A(1-cos^2A))/(cos^2A)`

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

= sin²A ×
`(sin^2A)/(cos^2A)`

= sin²A . tan²A

= right side , thus verified