Download App

Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $x+\frac{1}{x}=2 \cos \alpha$, then $x^n+\frac{1}{x^n}=$
  • A
    $2^n \cos \alpha$
  • B
    $2^n \cos n \alpha$
  • C
    $2 i \sin n \alpha$
  • ✓
    $2 \cos n \alpha$
✓

Answer

Correct option: D.
$2 \cos n \alpha$
(D)
$x+\frac{1}{x}=2 \cos \alpha$
Squaring on both sides, we get
$x^2+\frac{1}{x^2}+2=4 \cos ^2 \alpha$
$\Rightarrow x^2+\frac{1}{x^2}=4 \cos ^2 \alpha-2$
$\Rightarrow x^2+\frac{1}{x^2}=2\left(2 \cos ^2 \alpha-1\right)$
$=2 \cos 2 \alpha$
Similarly, $x^{ n }+\frac{1}{x^{ n }}=2 \cos n \alpha$

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 Trigonometry – II→Trigonometry – II — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

The co-ordinates of a point on $2 y^2=7 x$ whose parameter is -2 are
→
The lines 2x + y - 1 = 0 ax 3y - 3 = 0 and 3x + 2y - 2 = 0 are concurrent for
→
$\lim _{x \rightarrow 0} \frac{e^{\frac{1}{x}}}{e^{\left(\frac{1}{x}+1\right)}}=$
→
The directrix of the parabola $x^2 - 4x - 8y + 12 = 0$ is
→
The value of $\sin 18^{\circ}$ is
→
If the line through the points $(-2,6)$ and $(4,8)$ is perpendicular to the line passing through the points $(8,12)$ and $(x, 24)$, then the value of $x$ is
→
If $A+B=\frac{\pi}{4}$, then $(1+\tan A)(1+\tan B)=$
→
Equation of tangent to the circle $x^2+y^2=10$ at the point with abscissa 1 is
→
If $\text{z}=\frac{1}{(2+3\text{i})^2},$ then $|\text{z}|=$
→
If $f(x)=\left\{\begin{array}{cc}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\ \frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.$ is continuous in $[-1,1]$, then $p$ is equal to
→