If = 1 7 , ; = 1 3 , then 2 = - Vidyadip

MCQ

If $\tan \alpha = \frac{1}{7},\;\tan \beta = \frac{1}{3},$ then $\cos 2\alpha = $

A
$\sin 2\beta $
✓
$\sin 4\beta $
C
$\sin 3\beta $
D
None of these

✓

Answer

Correct option: B.

$\sin 4\beta $

b
(b) $\cos 2\alpha = \frac{{1 - {t^2}}}{{1 + {t^2}}} = \frac{{24}}{{25}}$ {Here $t = \tan \alpha $}

$\sin 2\beta = \frac{{2T}}{{1 + {T^2}}} = \frac{3}{5} \Rightarrow \cos 2\beta = \frac{4}{5}$ {$T = \tan \beta $}

$\therefore \,\,\sin 4\beta = 2\sin 2\beta \cos 2\beta $

$= 2.\frac{3}{5}.\frac{4}{5} = \frac{{24}}{{25}} = \cos 2\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 "M.C.Q (1 Marks)" from STD 11 - 3. trignometrical ratios,functions and identities→STD 11 - 3. trignometrical ratios,functions and identities — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $y = (1 + \tan A)(1 - \tan B)$ where $A - B = \frac{\pi }{4}$, then ${(y + 1)^{y + 1}}$ is equal to

If $a, b, c$ are in $AP,$ then the straight line $ax + by + c = 0$ will always pass through the point:

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is

The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -

Convert $-1 - i $ into polar form:

If $p(n): 2n < (1 \times 2 \times 3 \times ... \times n).$ Then the smallest positive integer for which $p(n)$ is true is:

Let $P(x)=1+x+x^2+x^3+x^4+x^5$. What is the remainder when $P\left(x^{12}\right)$ is divided by $P(x)$ ?

Extreame value of $1 + 4\, sin \theta + 3 \,cos \theta$ is

If the equation of the locus of a point equidistant from the points $({a_1},{b_1})$ and $({a_2},{b_2})$ is $({a_1} - {a_2})x + ({b_1} - {b_2})y + c = 0$, then the value of $‘c’$ is

The only statement among the following that is a tautology is.