Question

Tan2A - Sin2A=Sin2 A. Tan2A
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Answer 1

Step-by-step explanation:

${tan}^{2} \alpha - {sin}^{2} \alpha \\ = \dfrac{ {sin}^{2} \alpha }{ {cos}^{2} \alpha } - {sin}^{2} \alpha \\ = \dfrac{ {sin}^{2} \alpha - {sin}^{2} \alpha \: {cos}^{2} \alpha }{ {cos}^{2} \alpha } \\ = \dfrac{ {sin}^{2} \alpha \: (1 - {cos}^{2} \alpha ) }{ {cos}^{2} \alpha } \\ = {sin}^{2} \alpha \: (\dfrac{1 - {cos}^{2} \alpha }{ {cos}^{2} \alpha } ) \\ = {sin}^{2} \alpha \: \: ( \dfrac{ {sin}^{2} \alpha }{ {cos}^{2} \alpha } ) \\ = {sin}^{2} \alpha \: \: \: {tan}^{2} \alpha$