If 3 4 < < , then 2 +1 ^2 is equal to - Vidyadip

MCQ

If $\frac{3 \pi}{4}<\alpha<\pi$, then $\sqrt{2 \cot \alpha+\frac{1}{\sin ^2 \alpha}}$ is equal to

A
$-1+\cot \alpha$
B
$-1-\cot \alpha$
C
$1-\cot \alpha$
D
$1+\cot \alpha$

✓

Answer

(b) - 1 - cot
Explanation: We have:
$\begin{array}{l}\sqrt{2 \cot \alpha+\frac{1}{\sin ^2 \alpha}} \\ =\sqrt{\frac{2 \cos \alpha}{\sin \alpha}+\frac{1}{\sin ^2 \alpha}} \\ =\sqrt{\frac{2 \sin \alpha \cos \alpha+1}{\sin ^2 \alpha}} \\ =\sqrt{\frac{2 \sin \alpha \cos \alpha+\sin ^2 \alpha+\cos ^2 \alpha}{\sin ^2 \alpha}} \\ =\sqrt{\frac{(\sin \alpha+\cos \alpha)^2}{\sin ^2 \alpha}} \\ =\sqrt{(1+\cot \alpha)^2} \\ =|1+\cot \alpha| \\ =-(1+\cot \alpha)\left[\text { When } \frac{3 \pi}{4}<\alpha<\pi, \cot \alpha<-1 \Rightarrow \cot \alpha+1<0\right] \\ =-1-\cot \alpha\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Model Paper 8→Model Paper 8 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

For the following relation R = {(0, 0), (0, 1), (1, 1), (2, 1), (2, 2), (2, 0), (1, 0), (0, 2), (0, 1)}:

$\sec^2\text{x}=\frac{4\text{xy}}{(\text{x}+\text{y})^2}$ is true if and only if

$\text{x+y}\neq0$
$\text{x=y, x}\neq0$
$\text{x=y}$
$\text{x}\neq0,\text{y}\neq0$

The points A(2a, 4a), B(2a, 6a) and C(2a + 3a, 5a), a > 0 are the vertices of:

Choose the correct answer.
If $\text{f}(\text{x})=\begin{cases}\text{x}^{2}-1 & 0<\text{x}<2\\2\text{x}+3, & 2\geq\text{3}<3\end{cases}$ then the quadeatic equation whose roots are $\lim\limits_{\text{x} \rightarrow 2^{-}}\text{f}(\text{x})$ and $\lim\limits_{\text{x} \rightarrow 2^{+}}\text{f}(\text{x})$ is:

If $\text{y}=\frac{1+\frac{1}{\text{x}^{2}}}{1-\frac{1}{\text{x}^{2}}}$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:

$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
$\frac{1-\text{x}^{2}}{4\text{x}}$
$\frac{4\text{x}}{\text{x}^{2}-1}$

If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A - B) × (B - C) is:

The cartesian equation of the line is 3x + 1 = 6y - 2 = 1 - z then its direction ratio are:

Range of $\text{f(x)}=\frac{1}{1-2\cos\text{x}}$ is.

$\Big[\frac{1}{3}, 1\Big]$
$\Big[-1, \frac{1}{3}\Big]$
$(-\infty, -1]\cup\Big[\frac{1}{3},\infty\Big)$
$\Big[-\frac{1}{3}, 1\Big]$

If A − B = ∅, then relation between A and B is:

$ \lim \tan\text{x} = \text{x}→\frac{π}{2}$