If in a A B C, a^2 ^2 A-b^2-c^2=0, then - Vidyadip

MCQ

If in a $\triangle A B C, a^2 \cos ^2 A-b^2-c^2=0$, then

A
$\frac{\pi}{4}< A <\frac{\pi}{2}$
✓
$\frac{\pi}{2}< A <\pi$
C
$A=\frac{\pi}{2}$
D
$A<\frac{\pi}{4}$

✓

Answer

Correct option: B.

$\frac{\pi}{2}< A <\pi$

(B) $a^2 \cos ^2 A-b^2-c^2=0$
$\Rightarrow \cos ^2 A=\frac{ b ^2+ c ^2}{ a ^2}$
Since, $\cos ^2 A \leq 1$ i.e., $\cos ^2 A<1$
$\therefore \quad \frac{ b ^2+ c ^2}{ a ^2}<1 \Rightarrow b^2+ c ^2- a ^2<0$
$\therefore \quad \frac{ b ^2+ c ^2- a ^2}{2 bc }<0$ $\ldots .[\because 2 b c>0]$
$\therefore \cos A <0 \Rightarrow A \in\left(\frac{\pi}{2}, \pi\right)$

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 "MCQ" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

The radius of a circular plate is increasing at the rate of $0.01\ \text{cm/sec.}$ The rate of increase of its area when the radius is $12\ cm$, is:

Let $\text{f(x)}=\begin{vmatrix}\cos\text{x}&\text{x}&1\\2\sin\text{x}&\text{x}&2\text{x}\\\sin\text{x}&\text{x}&\text{x}\end{vmatrix},$ then $\lim_\limits{\text{x}\rightarrow0}\frac{\text{f(x)}}{\text{x}^2}$ is equal to:

If $\tan^{-1}\Big\{\frac{\sqrt{1+\text{x}^2}-\sqrt{1-\text{x}^2}}{\sqrt{1+\text{x}^2}+\sqrt{1-\text{x}^2}}\Big\}=\alpha,$ then $x^2 =$

The distance between the planes $2 x-2 y+z+3=0 \text { and } 4 x-4 y+2 z+5=0 \text { is }$

If $f : R \rightarrow R$ is given by $f(x) = 3x - 5$, then $f^{-1}(x)$

$\begin{vmatrix}\log_3512&\log_43\\\log_38&\log_49\end{vmatrix}\times\begin{vmatrix}\log_23&\log_83\\\log_34&\log_34\end{vmatrix}$

The rate at which the population of a city increses varies as the population present. Within the period of $30$ years, the population grew from $20$ lakhs to $40$ lakhs. Then, the population after a further period of $15$ years will be $($Take $\sqrt{2}=1.41)$

The converse of the contrapositive of $\mathrm{p} \rightarrow \mathrm{q}$ is

The area bounded by the curves $y=\log _e x$ and $y=\left(\log _e x\right)^2$ is

If the points $P (\overline{ a }+2 \overline{b}+\overline{ c }), Q (2 \overline{ a }+3 \overline{b})$ and $R (\overline{ b }+ t \overline{ c })$ are collinear, where $\overline{ a }, \overline{ b }, \overline{ c }$ are three non-coplanar vectors, then the value of $t$ is