( 2A + 1) ^2 A = - Vidyadip

MCQ

$(\sec 2A + 1){\sec ^2}A = $

A
$\sec A$
B
$2\sec A$
C
$\sec 2A$
✓
$2\sec 2A$

✓

Answer

Correct option: D.

$2\sec 2A$

d
(d) $(\sec 2A + 1){\sec ^2}A $

$= \left( {\frac{{1 + {{\tan }^2}A}}{{1 - {{\tan }^2}A}} + 1} \right)\,(1 + {\tan ^2}A)$

$ = \frac{{2\,(1 + {{\tan }^2}A)}}{{1 - {{\tan }^2}A}}$

$= 2\sec 2A.$

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 3. trignometrical ratios,functions and identities→3. trignometrical ratios,functions and identities — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

L is a variable line such that the algebraic sum of the distances of the points (1, 1), (2, 0) and (0, 2) from the line is equal to zero. The line L will always pass through:

The equation of the ellipse whose foci are $( \pm 5,\;0)$ and one of its directrix is $5x = 36$, is

Three identical dice are rolled. What is the probability that the same number will appear on each of them?

If P(n) = 2 + 4 + 6 +…+ 2n, n ∈ N ,P(k) = k(k + 1) + 2 ⇒ P(k + 1) = (k + 1)(k + 2) + 2 for all k ∈ N. So, we can conclude that P(n) = n (n + 1) 2 for:

If $33!$ is divisible by $2^n$,$n\in N$,then sum of all possible values of $n$ is-

Which of the following is true.

Let $N =$$\left| {\,\begin{array}{*{20}{c}}{28}&{25}&{38}\\{42}&{38}&{65}\\{56}&{47}&{83}\end{array}\,} \right|$, then the number of ways is which $N$ can be resol as a product of two divisors which are relatively prime is

If $\sin \left( {x + \frac{{4\pi }}{9}} \right) = a;\,$ $\frac{\pi }{9}\, < \,x\, < \,\frac{\pi }{3},$ then $\cos \left( {x + \frac{{7\pi }}{9}} \right)$ equals :-

If ${i^2} = - 1$, then the value of $\sum\limits_{n = 1}^{200} {{i^n}} $ is

If for some $x \in R$, the frequency distribution of the marks obtained by $20$ students in a test is
Marks $2$ $3$ $5$ $7$
Frequency $(x+1)^2$ $2x -5$ $x^2 -3x$ $x$
Then the mean of the marks is