_ r = 1 ^ 100 , 2^ r - 1 , 2^r is equal to - Vidyadip

MCQ

$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r - 1}}}}{{\cos \,{2^r}}}} $ is equal to

A
$tan\,2^{99} -tan\,1$
B
$tan\,2^{100}$
✓
$tan\,2^{100} -tan\,1$
D
none of these

✓

Answer

Correct option: C.

$tan\,2^{100} -tan\,1$

c
$\mathrm{T}_{\mathrm{x}}=\frac{\tan 2^{\mathrm{r}-1}}{\cos 2^{\mathrm{r}}}=\tan 2^{\mathrm{r}}-\tan 2^{\mathrm{r}-1}$

$ \Rightarrow \sum\limits_{r = 1}^{100} {{T_r} = \tan {2^{100}} - \tan 1} $

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 - Trigonometrical equations→STD 11 - Trigonometrical equations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The most frequently occurring data value in a data set is the $...........$

If the tangents $\&$ normals at the extremities of a focal chord of a parabola intersect at $(x_1, y_1) $ and $ (x_2, y_2) $ respectively, then :

The equation $\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} $, $x \in R$ has

If a point $(x,\;y) \equiv (\tan \theta + \sin \theta ,\;\tan \theta - \sin \theta )$, then locus of $(x, y)$ is

If the probabilities of boy and girl to be born are same, then in a $4$ children family the probability of being at least one girl, is

In the expansion of $(1 + x)^n.(1 + y)^n.(1 + z)^n$ the sum of the coefficients of the terms of degree $r$ is:

Which of the following equations of a circle has center at $(1, -3)$ and radius of $5:$

Let $f(x) = 4$ and $f'(x) = 4$, then $\mathop {\lim }\limits_{x \to 2} \,\frac{{xf(2) - 2f(x)}}{{x - 2}}$ equals

The equation of the ellipse with focus $(-1, 1),$ directrix $x - y + 3 = 0$ and eccentricity $\frac{1}{2}$ is:

The equations of the tangents to the circle ${x^2} + {y^2} = {a^2}$ parallel to the line $\sqrt 3 x + y + 3 = 0$ are