Question

1+tan^2A/1+cot^2A=tansquareA prove the following identity​

Answer 1

Answer:

To prove ,

$\frac{1 + {tan}^{2}A}{1 + {cot}^{2}A} = {tan}^{2}A$

We know That

$tanA = \frac{sin A }{cos A }$

And

$cotA = \frac{ cosA }{sin A} \:$

and

${sin}^{2}A+{cos}^{2}A=1$

Above properties of trigonometric functions will be used in proving the identity.

So, LHS

$\dfrac{1 + \frac{ {sin}^{2}A}{ {cos}^{2}A} }{1 + \frac{ {cos}^{2}A}{ {sin}^{2}A} } \\ \\ = \dfrac{\frac{ {cos}^{2}A + {sin}^{2}A}{ {cos}^{2}A} }{ \frac{ { {sin}^{2}A + {cos}^{2}A}}{ {sin}^{2}A} } \\ \\ = \dfrac{ \frac{1}{ { {cos}}^{2}A} }{ \frac{1}{ {sin}^{2}A} } \\ = \frac{ {sin}^{2}A}{ {cos}^{2}A} \\ = {tan}^{2} A \: = RHS$

Hence the required identity is proved.

Answer 2

Answer:

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