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What is the answer of tan square tita- sin square tita=tan square tita× sin square tita

What is the answer of tan square tita- sin square tita=tan square tita× sin square tita

Grade:10

1 Answers

Dhruvit Raithatha
32 Points
5 years ago
\text{To Prove That : }tan^2(A) - sin^2(A) = tan^2(A)\cdot\sin^2(A)\\\\ LHS = tan^2(A) - sin^2(A)\\ LHS = \frac{sin^2(A) - sin^2(A)cos^2(A)}{cos^2(A)}\\ LHS = \frac{sin^2(A) - sin^2(A)(1 - sin^2(A))}{cos^2(A)}\\ LHS = \frac{sin^2(A) - sin^2(A) + sin^4(A)}{cos^2(A)}\\ LHS = \frac{sin^4(A)}{cos^2(A)}\\\\ RHS = tan^2(A)\cdot\sin^2(A)\\ RHS = \frac{sin^4(A)}{cos^2(A)}\\\\ LHS = RHS

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