Question

Prove that tan²-A - sin² A = tan²-A. sin²’A. = -​

Answer 1

Answer:

Let us first find the value of left hand side (LHS) that is tan2A−sin2A as shown below:

       

tan2A−sin2A=cos2Asin2A−sin2A(∵tanx=cosxsinx)=cos2Asin2A−sin2Acos2A=sin2A(cos2A1−cos2A)=cos2Asin2A(1−cos2A)=tan2Asin2A=RHS(∵tanx=cosxsinx,1−cos2x=sin2

Answer 2

Step-by-step explanation:

Solution :-

On taking LHS :

tan² A - sin² A

=> (sin A / cos A )² - sin² A

=> ( sin² A / cos² A ) - sin² A

=> ( sin² A - sin² A cos² A) / cos² A

=> [sin² A ( 1- cos² A )] / cos² A

=> ( sin² A sin² A ) / cos² A

Since, sin² A + cos² A = 1

=> sin² A ( sin² A / cos² A )

=> sin² A tan²

=> tan² A sin² A

=> RHS

=> LHS = RHS

Hence, Proved.

Used Formulae:-

♦ tan A = sin A / cos A

♦ sin² A + cos² A = 1