MCQ
Choose the correct option. Justify your choice : $\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}= $
- A$\sec^2 \text{A}$
- B$-1$
- C$\cot^2 \text{A}$
- ✓$\tan^2 \text{A}$
✓
Answer
Correct option: D.
$\tan^2 \text{A}$
$\frac{1+\tan^2\text{A}}{1+\cot^2\text{A}}=\frac{\sec^2\text{A}-\tan^2\text{A}+\tan^2\text{A}}{\text{cosec}^2\text{A}-\cot^2\text{A}+\cot^2\text{A}}$
$=\frac{\sec^2\text{A}}{\text{cosec}^2\text{A}}=\frac{\frac{1}{\cos^2\text{A}}}{\frac{1}{\sin^2\text{A}}} $
$=\frac{\sin^2\text{A}}{\cos^2\text{A}}=\tan^2\text{A} $
$=\frac{\sec^2\text{A}}{\text{cosec}^2\text{A}}=\frac{\frac{1}{\cos^2\text{A}}}{\frac{1}{\sin^2\text{A}}} $
$=\frac{\sin^2\text{A}}{\cos^2\text{A}}=\tan^2\text{A} $
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