If 2 ^ - 1 ( x) = ^ - 1 (2 cosec x), then x = - Vidyadip

MCQ

If $2{\tan ^{ - 1}}(\cos x) = {\tan ^{ - 1}}(2{\rm{cosec }}x),$ then $x =$

A
$\frac{{3\pi }}{4}$
✓
$\frac{\pi }{4}$
C
$\frac{\pi }{3}$
D
None of these

✓

Answer

Correct option: B.

$\frac{\pi }{4}$

b
(b) We have $2$ ${\tan ^{ - 1}}(\cos x) = {\tan ^{ - 1}}(2\cos {\rm{ec}}x)$

==> ${\tan ^{ - 1}}\left( {\frac{{2\cos x}}{{1 - {{\cos }^2}x}}} \right)$$= {\tan ^{ - 1}}(2\,{\rm{cosec }}x)$

$\frac{{2\cos x}}{{{{\sin }^2}x}} = 2{\rm{cosec}}\,x \Rightarrow 2\cos x = 2\sin x$

or $\sin x = \cos x$

$ \Rightarrow x = \frac{\pi }{4}$.

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 12 - 2. inverse trigonometric function→STD 12 - 2. inverse trigonometric function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

There are two value of a which makes the determinant $\triangle=\begin{vmatrix}1&-2&5\\2&\text{a}&-1\\0&4&2\text{a}\end{vmatrix}$ equal to $86$. The sum of these two values is:

Let $[t]$ denote the greatest integer less than or equal to $t$. Let $\mathrm{f}:[0, \infty) \rightarrow \mathrm{R}$ be a function defined by $f(x)=\left[\frac{x}{2}+3\right]-[\sqrt{x}]$. Let $S$ be the set of all points in the interval $[0,8]$ at which $\mathrm{f}$ is not continuous. Then $\sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to............

The value of $\int_{\,0}^{\,\pi /2} {\frac{{{2^{\sin x}}}}{{{2^{\sin x}} + {2^{\cos x}}}}dx} $ is

The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ - 2}\\{ - 2}&2&{ - 1}\end{array}} \right]$is

$\int_{ - \pi /2}^{\pi /2} {{{\sin }^2}x\,dx = } $

One maximum point of ${\sin ^p}x{\cos ^q}x$ is

Choose the correct answer from the given four options.
The locus represented by xy + yz = 0 is:

If ${I_n} = \int_0^\infty {{e^{ - x}}{x^{n - 1}}dx,} $ then $\int_0^\infty {{e^{ - \lambda x}}{x^{n - 1}}dx = } $

A parallelopiped is formed by planes drawn through the point $(2, 3, 5)$ and $(5, 9, 7)$ parallel to the coordinate planes. The length of a diagonal of the parallelopiped is:

The circumference of a circle is measured as $28\ cm$ with an error of $0.01\ cm$. The percentage error in the area is: