_ ^ cosec - cosec + ;d = - Vidyadip

MCQ

$\int_{}^{} {\frac{{{\rm{cosec}}\theta - \cot \theta }}{{{\rm{cosec}}\theta + \cot \theta }}} \;d\theta = $

✓
$2{\rm{cosec}}\theta - 2\cot \theta - \theta + c$
B
$2\,{\rm{cosec}}\theta - 2\cot \theta + \theta + c$
C
$2\,{\rm{cosec}}\theta + 2\cot \theta - \theta + c$
D
None of these

✓

Answer

Correct option: A.

$2{\rm{cosec}}\theta - 2\cot \theta - \theta + c$

a
(a)$\int_{}^{} {\frac{{{\rm{cosec}}\theta - \cot \theta }}{{{\rm{cosec}}\theta + \cot \theta }}\,d\theta } = \int_{}^{} {{{({\rm{cosec}}\theta - \cot \theta )}^2}d\theta } $
$ = \int_{}^{} {{\rm{cose}}{{\rm{c}}^2}\theta \,d\theta } + \int_{}^{} {{{\cot }^2}\theta \,d\theta } - 2\int_{}^{} {{\rm{cosec}}\theta \cot \theta \,d\theta } $
$ = \int_{}^{} {(2{\rm{cose}}{{\rm{c}}^2}\theta - 1)\,d\theta } - 2\int_{}^{} {{\rm{cosec}}\theta \cot \theta \,d\theta } $
$ = 2{\rm{cosec}}\theta - 2\cot \theta - \theta + c.$

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

Given $f(x) = b ([x]^2 + [x]) + 1$ for $x \geq -1$ and $= sin (\pi (x+a) )$ for $x < -1$

where $[x]$ denotes the integral part of $x$ ,

then for what values of $a, b$ the function is continuous at $x = -1$ ?

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{{x^2}}} - \cos x}}{{{x^2}}} = $

A circle is drawn to cut a chord of length $2a$ units along $X$-axis and to touch the $Y$-axis. The locus of the centre of the circle is

Let $\{x\}$ denote the fractional part of $\mathrm{x}$ and $f(x)=\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x \neq 0$. If $L$ and $\mathrm{R}$ respectively denotes the left hand limit and the right hand limit of $f(x)$ at $x=0$, then $\frac{32}{\pi^2}\left(L^2+R^2\right)$ is equal to..........................

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$, then which of the following is correct?

The number of ways, in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together, is

Equation of curve passing through $(3, 9)$ which satisfies the differential equation $\frac{{dy}}{{dx}} = x + \frac{1}{{{x^2}}}$, is

$\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{{\Sigma {n^2}}}{{{n^3}}}} \right] = $

If $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has local maximum and minimum at $x = p$ and $x = q$ , respectively, then $(p, q)$ equals

Solve the system of equations : $ 2 x+5 y=1 ; 3 x+2 y=7$