Download App

Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
In $\triangle A B C$, if $(a+b+c)(a-b+c)=3 a c$, then
  • ✓
    $\angle B =60^{\circ}$
  • B
    $\angle B =30^{\circ}$
  • C
    $\angle C =60^{\circ}$
  • D
    $\angle A +\angle C =90^{\circ}$
✓

Answer

Correct option: A.
$\angle B =60^{\circ}$
(A) $(a+b+c)(a-b+c)=3 a c$
$\begin{array}{l}\Rightarrow a^2+2 a c+c^2-b^2=3 a c \\ \Rightarrow a^2+c^2-b^2=a c\end{array}$
But $\cos B =\frac{ a ^2+ c ^2- b ^2}{2 ac }=\frac{1}{2} \Rightarrow B=60^{\circ}$

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

If the p.d.f. of a random variable X is
$\mathrm{f}(x)=\left\{\begin{array}{cc}0.5 x, & 0 \leq x \leq 2 \\ 0, & \text { otherwise }\end{array}\right.$
then the value of $\mathrm{P}(0.5 \leq \mathrm{X} \leq 1.5)$ is
→
The ratio of the areas between the curves $\text{y}=\cos\text{x}$ and $\text{y}=\cos2\text{x}$ and $x-$axis from $x = 0$ to $x = 0$ to $\text{x}=\frac{\pi}{3}$
→
If $f : R \rightarrow R$ is given by $f(x) = 3x - 5$, then $f^{-1}(x)$
→
The derivative of $f(\sec x)$ with respect to $g(\tan x)$ at $x=\frac{\pi}{4}$, where $f^{\prime}(\sqrt{2})=4$ and $g^{\prime}(1)=2$, is
→
The equation $x^2-7 x y+12 y^2=0$ represents
→
If $\sin 2 \theta=\cos 3 \theta$ and $\theta$ is an acute angle, then $\sin \theta$ is equal to
→
$\int_0^{\pi / 2} \frac{\sin x}{1+\cos ^2 x} d x$ has the value
→
Let $\overline{ a }$ and $\overline{ b }$ be two unit vectors. If the vectors $\overline{ c }=\overline{ a }+2 \overline{b}$ and $\overline{ d }=5 \overline{ a }-4 \overline{b}$ are perpendicular to each other, then the angle between $\overline{ a }$ and $\overline{ b }$ is
→
Which of the following is true?
→
If a line makes angles $45^{\circ}, 60^{\circ}$ and $60^{\circ}$ with the $X , Y$ and Z -axes respectively, then its direction cosines are
→