If =1 7 , =1 3 , then 2 is equal to: - Vidyadip

MCQ

If $\tan\alpha=\frac{1}{7},\tan\beta=\frac{1}{3},$ then $\cos2\alpha$ is equal to:

A
$\sin2\beta$
✓
$\sin4\beta$
C
$\sin3\beta$
D
$\cos2\beta$

✓

Answer

Correct option: B.

$\sin4\beta$

Given that, $\tan\alpha=\frac{1}{7}$ and $\tan\beta=\frac{1}{3}$
$\cos2\alpha=\frac{1-\tan^2\alpha}{1+\tan^2\alpha}=\frac{1-\Big(\frac{1}{7}\Big)^2}{1+\Big(\frac{1}{7}\Big)^2}=\frac{1-\frac{1}{49}}{1+\frac{1}{49}}$
$=\frac{48}{50}=\frac{24}{25}$
Now $\tan2\beta=\frac{2\tan\beta}{1-\tan^2\beta}=\frac{2\times\frac{1}{3}}{1-\frac{1}{9}}=\frac{\frac{2}{3}}{\frac{8}{9}}=\frac{2}{3}\times\frac{9}{8}=\frac{3}{4}$
$\therefore\tan^2\beta=\frac{3}{4}$
$\sin4\beta=\frac{2\tan2\beta}{1+\tan^22\beta}$
$=\frac{2\times\frac{3}{4}}{1+\Big(\frac{3}{4}\Big)^2}$
$=\frac{\frac{3}{2}}{1+\frac{9}{16}}$
$=\frac{3}{2}\times\frac{16}{25}$
$=\frac{24}{25}$
$\cos2\alpha=\sin4\beta=\frac{24}{25}$
Hence, the correct option is $(b).$

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 Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $\cos x + \cos y + \cos \alpha = 0$ and $\sin x + \sin y + \sin \alpha = 0,$ then $\cot \,\left( {\frac{{x + y}}{2}} \right) = $

The value of $(1+\text{i})^4+(1-\text{i})^4$ is:

What is the value of $\lim_\limits{\text{x} \rightarrow 0}\frac{\text{e}^\text{X}(\sin^2\text{x})}{\text{x}^3}?$

The acute angle between two straight lines passing through the point $M(- 6, - 8)$ and the points in which the line segment $2x + y + 10 = 0$ enclosed between the co-ordinate axes is divided in the ratio $1 : 2 : 2$ in the direction from the point of its intersection with the $x -$ axis to the point of intersection with the $y -$ axis is :

The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \ldots .$ to $\infty$ is equal to

The ratio of coefficient of $x^2$ to coefficient of $x^{10}$ in the expansion of ${\left( {{x^5} + {{4.3}^{ - {{\log }_{\sqrt 3 }}\sqrt {{x^3}} }}} \right)^{10}}$ is

The area of the triangle formed by joining the origin to the points of intersection of the line $x\sqrt 5 + 2y = 3\sqrt 5 $ and circle ${x^2} + {y^2} = 10$ is

The chance of throwing at least $9$ in a single throw with two dice, is

Find the equation of line parallel to $y-$axis and passing through $(3, 4):$

The common chord of two intersecting circles $c_1\,\, \& \,\,c_2$ can be seen from their centres at the angles of $90^o$ and $60^o$ respectively . If the distance between their centres is equal to $\sqrt{3} + 1$ then the radii of $c_1\,\, \& \,\,c_2$ are :