[ 3 , ^ - 1 ( 1 5 ) ] = - Vidyadip

MCQ

$\sin {\rm{ }}\left[ {3\,{{\sin }^{ - 1}}\left( {\frac{1}{5}} \right)} \right] = $

✓
$71/125$
B
$74/125$
C
$3/5$
D
$1/2$

✓

Answer

Correct option: A.

$71/125$

a
(a) $\sin \left[ {3{{\sin }^{ - 1}}\frac{1}{5}} \right]$

$ = \sin \left[ {{{\sin }^{ - 1}}\left\{ {3{\rm{ }}\left( {\frac{1}{5}} \right) - 4{\rm{ }}{{\left( {\frac{1}{5}} \right)}^3}} \right\}} \right]$

$ = \sin \left[ {{{\sin }^{ - 1}}\left\{ {\frac{3}{5} - \frac{4}{{125}}} \right\}} \right]$

$ = \sin \left[ {{{\sin }^{ - 1}}\left( {\frac{{75 - 4}}{{125}}} \right)} \right]$

$ = \sin \left[ {{{\sin }^{ - 1}}\frac{{71}}{{125}}} \right] = \frac{{71}}{{125}}$.

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 $(b+c),(c+a),(a+b)$ are in $H.P$ , then $a^2,b^2,c^2$ are in.......

If $s$ is the sum of an infinite $G.P.$, the first term $a$ then the common ratio $r$ given by

The total number of two digit numbers $'n',$ such that $3^{n}+7^{n}$ is a multiple of $10 ,$ is ..... .

A curve is such that the area of the region bounded by the co-ordinate axes, the curve $\&$ the ordinate of any point on it is equal to the cube of that ordinate. The curve represents

For each $x\,\in R,$ let $[x]$ be the greatest integer less than or equal to $x.$ Then $\mathop {\lim }\limits_{x \to {0^ + }} \frac{{x([x] + [x])\,\sin \,[x]}}{{\left| x \right|}}$ is equal to

If $\int_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}} d x=a+b \sqrt{2}+c \sqrt{3}$, where $a, b, c$ are rational numbers, then $2 a+3 b-4 c$ is equal to :

Let $A$ be a nonsingular square matrix of order $3 \times 3 .$ Then $|adj\, A|$ is equal to

For the function $f(x)=(\cos x)-x+1, x \in R,$ between the following two statements $(S_1) f(x)=0$ for only one value of $x$ is $[0, \pi]. (S_2) f(x)$ is decreasing in $\left[0, \frac{\pi}{2}\right]$ and increasing in $\left[\frac{\pi}{2}, \pi\right]$.

If $A$ is a square matrix of order $3$ such that $ \operatorname{det}(\mathrm{A})=3 \text { and } $ $ \operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2 \mathrm{~A})^{-1}\right)\right)\right)\right)\right)=2^{\mathrm{m}} 3^{\mathrm{n}},$ then $m+\mid 2 n$ is equal to:

If $f(x) = \frac{x}{{x - 1}}$, then $\frac{{f(a)}}{{f(a + 1)}} = $