Question

Tan^2A -sin^2A=sin^2a Tan^2A​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the identity

sin²A = 1 - cos²A , tanA = $\frac{sinA}{cosA}$

Consider the left side

tan²A - sin²A

= $\frac{sin^2A}{cos^2A}$ - sin²A

$\frac{sin^2A-sin^2Acos^2A}{cos^2A}$

= $\frac{sin^2A(1-cos^2A)}{cos^2A}$

= $\frac{sin^2A.sin^2A}{cos^2A}$

= sin²A × $\frac{sin^2A}{cos^2A}$

= sin²A . tan²A

= right side , thus verified