1+ ^2 A 1+ ^2 A =? - Vidyadip

MCQ

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

A
$\tan ^2 \mathring A$
B
$\sec ^2 \mathring A$
C
$\operatorname{cosec}^2 \mathring A$
✓
$\cot ^2 \mathring A$

✓

Answer

Correct option: D.

$\cot ^2 \mathring A$

$\cot ^2 \mathrm{~A}$$\frac{1+\cot ^2 \mathrm{~A}}{1+\tan ^2 \mathrm{~A}}$
$=\frac{\operatorname{cosec}^2 \mathrm{~A}}{\sec ^2 \mathrm{~A}}$
$=\frac{\frac{1}{\sin ^2 \mathrm{~A}}}{\frac{1}{\cos ^2 \mathrm{~A}}}$
$=\frac{\cos ^2 \mathrm{~A}}{\sin ^2 \mathrm{~A}}$
$=\cot ^2 \mathrm{~A}$

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