MCQ
$\sqrt{\frac{1+\cos A}{1-\cos A}}=?$
- Acosec A - cot A
- B$-\operatorname{cosec} A \cot A$
- ✓$\operatorname{cosec} A+\cot A$
- D$\operatorname{cosec} A \cot A$
✓
Answer
Correct option: C.
$\operatorname{cosec} A+\cot A$
(c) $\operatorname{cosec} A +\cot A$
Explanation : $\sqrt{\frac{1+\cos A}{1-\cos A}}=\sqrt{\frac{(1+\cos A)}{(1-\cos A)} \times \frac{(1+\cos A)}{(1+\cos A)}}=\frac{(1+\cos A)}{\sqrt{1-\cos ^2 A}}=\frac{(1+\cos A)}{\sqrt{\sin ^2 A}}$
$=\frac{(1+\cos A)}{\sin A}=\left(\frac{1}{\sin A}+\frac{\cos A}{\sin A}\right)=(\operatorname{cosec} A+\cot A)$
Explanation : $\sqrt{\frac{1+\cos A}{1-\cos A}}=\sqrt{\frac{(1+\cos A)}{(1-\cos A)} \times \frac{(1+\cos A)}{(1+\cos A)}}=\frac{(1+\cos A)}{\sqrt{1-\cos ^2 A}}=\frac{(1+\cos A)}{\sqrt{\sin ^2 A}}$
$=\frac{(1+\cos A)}{\sin A}=\left(\frac{1}{\sin A}+\frac{\cos A}{\sin A}\right)=(\operatorname{cosec} A+\cot A)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Two circles touch each other externally at $P. AB$ is a common tangent to the circles touching them at $A$ and $B$. The value of $\angle\text{APB}$ is :
→On increasing the diameter of a circle by 40%, its area will be increased by:
If the diagonals of a quadrilateral divide each other proportionally then it is a:
The height of a tower is $100m$. When the angle of elevation of the sun changes from $30^\circ$ to $45^\circ ,$ the shadow of the tower becomes $x$ metres less. The value of $x$ is :
→If $\frac{x}{3}=2 \sin A, \frac{y}{3}=2 \cos A$, then the value of $x^2+y^2$ is:
→In the given figure, the shaded area is
Choose the correct answer from the given four options in the following questions Which of the following equations has no real roots?
Choose the correct answer from the given four options in the following questions:
Which of the following equations has two distinct real roots?
Which of the following equations has two distinct real roots?
A polynomial of degree $..........$ is called a linear polynomial :
→If an event cannot occur then its probability is