MCQ
$\sqrt{\frac{1+\cos\text{A}}{1-\cos\text{A}}}=?$
- A$\text{cosec }\text{A}-\cot\text{A}$
- ✓$\text{cosec }\text{A}+\cot\text{A}$
- C$\text{cosec }\text{A}\cot\text{A}$
- DNone of these.
✓
Answer
Correct option: B.
$\text{cosec }\text{A}+\cot\text{A}$
$\sqrt{\frac{1+\cos\text{A}}{1-\cos\text{A}}}=\sqrt{\frac{1+\cos\text{A}}{1-\cos\text{A}}\times\frac{1+\cos\text{A}}{1+\cos\text{A}}}$
$=\sqrt{\frac{(1+\cos\text{A})^2}{1-\cos^2\text{A}}}$
$=\sqrt{\frac{(1+\cos\text{A})^2}{\sin^2\text{A}}}$
$=\frac{1+\cos\text{A}}{\sin\text{A}}$
$=\frac{1}{\sin\text{A}}-\frac{\cos\text{A}}{\sin\text{A}}$
$=\text{cosec }\text{A}+\cot\text{A}$
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