Question

tan? A - sin? A = sin? A tan2 A
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Answer 1

Step-by-step explanation:

Let us first find the value of left hand side (LHS) that is tan 2A−sin2A as shown below:

tan ²A−sin ²A

= cos ²A/sin²A −sin ²A(∵tanx= sinx/cosx )

=sin²A−sin²Acos²A/cos²

=sin ²A( 1−cos²A/cos ²A )

= sin ²A/cos ²A (1−cos ² A)

=tan²Asin ²A

=RHS(∵tanx= sinx/ccos ,1−cos ² x=sin² x)

Since LHS=RHS,

Hence, tan ² A−sin² A=tan²Asin²A.