If A 2 = 3 2 , then 1 + A 1 - A = - Vidyadip

MCQ

If $\tan \frac{A}{2} = \frac{3}{2},$ then $\frac{{1 + \cos A}}{{1 - \cos A}} = $

A
$ - 5$
B
$5$
C
$9/4$
✓
$4/9$

✓

Answer

Correct option: D.

$4/9$

d
(d) Given that $\tan \frac{A}{2} = \frac{3}{2}$.

$\frac{{1 + \cos A}}{{1 - \cos A}} $

$= \frac{{2{{\cos }^2}\frac{A}{2}}}{{2{{\sin }^2}\frac{A}{2}}} $

$= {\cot ^2}\frac{A}{2} = {\left( {\frac{2}{3}} \right)^2} = \frac{4}{9}$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the straight lines , $ax + amy + 1 = 0 $, $b x + (m + 1) b y + 1 = 0$ and $cx + (m + 2)cy + 1 = 0$,$ m \ne 0$ are concurrent then $a, b, c$ are in :

A bag contains $16$ coins of which two are counterfeit with heads on both sides. The rest are fair coins. One coin is selected at random from the bag and tossed. The probability of getting a head is

$\int {\frac{{1 - {x^7}}}{{x\left( {1 + {x^7}} \right)}}} \,dx$ equals

If function $f(x) = \frac{1}{2} - \tan \left( {\frac{{\pi x}}{2}} \right)$; $( - 1 < x < 1)$ and $g(x) = \sqrt {3 + 4x - 4{x^2}} $, then the domain of $gof$ is

Let $\alpha, \beta$ and $\gamma$ be real numbers such that the system of linear equations

$x+2 y+3 z=\alpha$

$4 x+5 y+6 z=\beta$

$7 x+8 y+9 z=\gamma-$

is consistent. Let $| M |$ represent the determinant of the matrix

$M=\left[\begin{array}{ccc}\alpha & 2 & \gamma \\ \beta & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$

Let $P$ be the plane containing all those $(\alpha, \beta, \gamma)$ for which the above system of linear equations is consistent, and $D$ be the square of the distance of the point $(0,1,0)$ from the plane $P$.

($1$) The value of $| M |$ is

($2$) The value of $D$ is

If $f(x) = \sqrt {{x^2} + x} + \frac{{{{\tan }^2}\alpha }}{{\sqrt {{x^2} + x} }},\alpha \in (0,\pi /2),x > 0$ then value of $f(x)$ is greater than or equal to-

Let $x_n, y_n, z_n, w_n$ denotes $n^{th}$ terms of four different arithmatic progressions with positive terms. If $x_4 + y_4 + z_4 + w_4 = 8$ and $x_{10} + y_{10} + z_{10} + w_{10} = 20,$ then maximum value of $x_{20}.y_{20}.z_{20}.w_{20}$ is-

Let $\alpha $ and $\beta $ be the roots of $a{x^2} + bx + c = 0$, then $\mathop {\lim }\limits_{x \to \alpha } \frac{{1 - \cos (a{x^2} + bx + c)}}{{{{(x - \alpha )}^2}}}$ is equal to

Let $f (x)$ be diffrentiable at $x = h$ then $\mathop {\lim }\limits_{x \to h} \,\frac{{(x + h)\,f(x)\, - 2h\,f(h)}}{{x - h}}$ is equal to

If $5\tan \theta = 4,$ then $\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 2\cos \theta }} = $