If (2 ^ - 1 x) = 1 9 , then x = - Vidyadip

MCQ

If $\cos (2{\sin ^{ - 1}}x) = \frac{1}{9},$ then $x = $

A
Only $ \frac{2}{3}$
B
Only$ \frac{-2}{3}$
✓
$\frac{2}{3}, \frac{-2}{3}$
D
Neither $\frac{2}{3}$ nor $\frac{-2}{3}$

✓

Answer

Correct option: C.

$\frac{2}{3}, \frac{-2}{3}$

c
(c) $\cos (2{\sin ^{ - 1}}x) = \frac{1}{9}$

$ \Rightarrow \cos ({\sin ^{ - 1}}2x\sqrt {1 - {x^2}} ) = \frac{1}{9}$

==>$\cos ({\cos ^{ - 1}}\sqrt {1 - 4{x^2} + 4{x^4}} ) = \frac{1}{9}$

==> $1 - 2{x^2} = \frac{1}{9} \Rightarrow 2{x^2} = 1 - \frac{1}{9} = \frac{8}{9}$

==> ${x^2} = \frac{4}{9} \Rightarrow x = \pm \frac{2}{3}$.

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 2. inverse trigonometric function→2. inverse trigonometric function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the system of linear equations, $x+y+z =6$ ; $x+2 y+3 z =10$ ; $3 x+2 y+\lambda z =\mu$ has more two solutions, then $\mu-\lambda^{2}$ is equal to

$\int_{}^{} {x{{\sin }^2}x\;dx = } $

If the matrix AB is zero, then:

It is not necessary that either A = 0 or, B = 0
A = 0 or B = 0
A = 0 and B = 0
All the above statements are wrong

If $sin^{-1}\,\theta = sin^{-1}(sin\,5)$ then $\theta $ is

If $\vec{b}$ and $\vec{c}$ are any two non-collinear unit vectors and $\vec{a}$ is any vector, then find the value of $(\vec{a} \cdot \vec{b}) \vec{b}+(\vec{a} \cdot \vec{c}) \vec{c}+\frac{\vec{a} \cdot(\vec{b} \times \vec{c})}{|\vec{b} \times \vec{c}|} \cdot(\vec{b} \times \vec{c})$.

The perimeter of a triangle with sides $3i + 4j + 5k,\,$ $4i - 3j - 5k$ and $7i +j$ is

Let $\vec b$ and $\vec c$ be non-collinear vector satisfying $\vec a \times \left( {\vec b \times \vec c} \right) + \left( {\vec a.\vec b} \right)\vec b = \left( {4 - 2x - \sin y} \right)\vec b + \left( {{x^2} - 1} \right)\vec c$ and $\left( {\vec c.\vec c} \right)\vec a = \vec c$ , then $x$ is equal to

$\int_{ - 1}^1 {x{{\tan }^{ - 1}}x\,dx} $ equals

Let $S$ be the set containing all $3 \times 3$ matrices with entries from $\{-1,0,1\}$. The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A ^{ T } A$ is $6$ is.

$\int_{}^{} {\frac{{x - 1}}{{(x - 3)(x - 2)}}dx = } $