Question

Evaluate 1+tansquareA by 1+cotsquareA

Answer 1

The answer of $\frac{1+\tan^{2} A}{1+\cot ^{2} A}$ is $\tan ^{2}A$

Step-by-step explanation:

The given equation is $\frac{1+\tan ^{2}A}{1+\cot ^{2}A}$

As we know that, $\tan A = \frac{\sin A}{\cos A}$

and  $\cot A = \frac{\cos A}{\sin A}$

$=> F(A) = \frac{1+\left (\frac{\sin A}{\cos A}  \right )^{2}}{1+\left (\frac{\cos A}{\sin A}  \right )^{2}}$

    $F(A) = \frac{\frac{\sin ^{2} A +\cos ^{2} A}{\cos ^{2} A}}{\frac{\sin ^{2} A+\cos ^{2} A}{\sin ^{2} A}}$

    $F(A) = \frac{\frac{1}{\cos ^{2}}}{\frac{1}{\sin ^{2}}}$

    $F(A) = \frac{\sin ^{2} A}{\cos ^{2} A}$

    $F(A) = \tan^{2} A$

The answer of $\frac{1+\tan^{2} A}{1+\cot ^{2} A}$ is $\tan ^{2}A$