Question

Prove That:
1-tan²A/1+tan²A=cos²A-sin²A 

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Answer 1

LHS:

$\frac{1 - {tan}^{2} a}{1 + {tan}^{2}a }$

$\frac{1 - \frac{ {sin}^{2}a }{ {cos}^{2} a} }{1 + \frac{ {sin}^{2}a }{ {cos}^{2} a} }$

$\frac{ \frac{ {cos}^{2}a - {sin}^{2}a }{ {cos}^{2}a } }{ \frac{ {cos}^{2}a + {sin}^{2} a }{ {cos}^{2}a } }$

$\frac{ {cos}^{2}a - {sin}^{2} a }{ {cos}^{2} a + {sin}^{2} a}$

${cos}^{2} a - {sin}^{2} a \: \: (here \: {sin}^{2} a + {cos}^{2}a = 1)$

LHS = RHS

hence proved

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