Download App

Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
$\tan ^{-1}\left\{\frac{3 a ^2 x-x^3}{ a \left( a ^2-3 x^2\right)}\right\}=$
  • ✓
    $3 \tan ^{-1} \frac{x}{a}$
  • B
    $2 \tan ^{-1} \frac{x}{a}$
  • C
    $\tan ^{-1} \frac{x}{a}$
  • D
    $\tan ^{-1} \frac{ a }{x}$
✓

Answer

Correct option: A.
$3 \tan ^{-1} \frac{x}{a}$
(A) $\tan ^{-1}\left\{\frac{3 a ^2 x-x^3}{ a \left( a ^2-3 x^2\right)}\right\}=\tan ^{-1}\left\{\frac{3 a ^2 x-x^3}{ a ^3-3 ax ^2}\right\}$
$=\tan ^{-1}\left(\frac{3\left(\frac{x}{ a }\right)-\left(\frac{x}{ a }\right)^3}{1-3\left(\frac{x}{ a }\right)^2}\right)$
Put $\frac{x}{ a }=\tan \theta$
$\therefore \quad$ The given expression becomes
$\tan ^{-1}\left(\frac{3 \tan \theta-\tan ^3 \theta}{1-3 \tan ^2 \theta}\right)=\tan ^{-1}(\tan 3 \theta)$
$=3 \theta=3 \tan ^{-1} \frac{x}{ a }$

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

Let D be the middle point of the side BC of a triangle ABC . If the triangle ADC is equilateral, then $a^2: b^2: c^2$ is equal to
→
The area bounded by y = √x and line x = 2y + 3, X-axis in first quadrant is
→
If $c^2=a^2+b^2$, then $4 s(s-a)(s-b)(s-c)=$
→
Let $f(x)=x^3-6 x^2+9 x+18$, then $f(x)$ is strictly decreasing in
→
The area of smaller part between the circle $x^2+y^2=4$ and the line $x=1$ is
→
$\int_0^{\log 5} \frac{e^x \sqrt{e^x-1}}{e^x+3} \cdot d x=$
→
If $\text{y}=\frac{1}{1+\text{x}^{\text{a}-\text{b}}+\text{x}^{\text{c}-\text{b}}}+\frac{1}{1+\text{x}^{\text{b}-\text{c}}+\text{x}^{\text{a}-\text{c}}}+\frac{1}{1+\text{x}^{\text{b}-\text{a}}+\text{x}^{\text{c}-\text{a}}},$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:
→
The solution of the differential equation $2\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}=3$ resresents:
→
If $A, B$ are two $n \times n$ non$-$singular matrices, then
→
The inverse of the function $\text{f}:\text{R}\rightarrow\{\text{x}\in\text{R}:\text{x}<1\}$ given by $\text{f(x)}=\frac{\text{e}^{\text{x}}-\text{e}^{-\text{x}}}{\text{e}^\text{x}+\text{e}^{-\text{x}}}$ is:
→