Download App

STD 11 - 3. trignometrical ratios,functions and identities — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 3. trignometrical ratios,functions and identities4 Marks
MCQ
$\frac{{\cos A}}{{1 - \sin A}} = $
  • A
    $\sec A - \tan A$
  • B
    ${\rm{cosec}}\,A + \cot A$
  • C
    $\tan \left( {\frac{\pi }{4} - \frac{A}{2}} \right)$
  • ✓
    $\tan \left( {\frac{\pi }{4} + \frac{A}{2}} \right)$
✓

Answer

Correct option: D.
$\tan \left( {\frac{\pi }{4} + \frac{A}{2}} \right)$
d
(d) $\frac{{\cos A}}{{1 - \sin A}} = \frac{{\cos A(1 + \sin A)}}{{{{\cos }^2}A}} = \frac{{(1 + \sin A)}}{{\cos A}}$

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

$= \frac{{\cos \frac{A}{2} + \sin \frac{A}{2}}}{{\cos \frac{A}{2} - \sin \frac{A}{2}}}$

$ = \frac{{1 + \tan \frac{A}{2}}}{{1 - \tan \frac{A}{2}}}$, $\left( {{\rm{Dividing}}\,{N^r}\,{\rm{and}}\,{D^r}\,{\rm{by}}\,\cos \frac{A}{2}} \right)$

$ = \tan \left( {\frac{\pi }{4} + \frac{A}{2}} \right)$.

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

It is $5 : 2$ against a husband who is $65$ years old living till he is $85$ and $4 : 3$ against his wife who is now $58$, living till she is $78$. If the probability that atleast one of them will be alive for $20$ years, is $'k'$, then the value of $'49k'$ -
→
$\int_{}^{} {\frac{{{e^{2x}} - 1}}{{{e^{2x}} + 1}}} \;dx = $
→
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
→
If $^n{C_{r - 1}} = 36,{\;^n}{C_r} = 84$ and $^n{C_{r + 1}} = 126$, then the value of $r$ is
→
If $A_1, A_3, ..... A_{2n - 1}$ are $n$ skew symmetric matrices of same order then $B =$$\sum\limits_{r = 1}^n {(2r - 1){{({A_{2r - 1}})}^{2r - 1}}} $ will be
→
The remainder, when $7^{103}$ is divided by $17$ is $..........$.
→
If $A,B,C,D$are the points $(2, 3, -1),(3, 5, -3), (1, 2, 3), (3, 5, 7)$ respectively, then the angle between $AB$ and $CD$ is
→
Let $a,b,c$ be real numbers $a \ne 0$. If $\alpha $is a root ${a^2}{x^2} + bx + c = 0$, $\beta $ is a root of ${a^2}{x^2} - bx - c = 0$ and $0 < \alpha < \beta $, then the equation ${a^2}{x^2} + 2bx + 2c = 0$ has a root $\gamma $ that always satisfies
→
Let $[t]$ denote the greatest integer less than or equal to $t.$ Then, the value of the integral $\int\limits_{0}^{1}\left[-8 x^{2}+6 x-1\right] d x$ is equal to
→
Let $a_1, a_2, \ldots, a_n$ be $n$ non-zero real numbers, of which $p$ are positive and remaining are negative. The number of ordered pairs $(j, k), j < k$, for which $a_j a_k$ is positive, is $55$ . Similarly, the number of ordered pairs $(j, k), j < k$, for which $a_j a_k$ is negative, is $50$ . Then, the value of $p^2+(n-p)^2$ is
→