Solve: 4 ^ -1 x= - ^ -1 x - Vidyadip

Question

Solve:
$4\sin^{-1}\text{x}={\pi}-\cos^{-1}\text{x}$

✓

Answer

$4\sin^{-1}\text{x}={\pi}-\cos^{-1}\text{x}$
$\Rightarrow4\sin^{-1}\text{x}={\pi}-\Big(\frac{\pi}{2}-\sin^{-1}\text{x}\Big)$
$\Big[\because\ \cos^{-1}\text{x}=\frac{\pi}{2}-\sin^{-1}\text{x}\Big]$
$\Rightarrow4\sin^{-1}\text{x}=\frac{\pi}{2}+\sin^{-1}\text{x}$
$\Rightarrow3\sin^{-1}\text{x}=\frac{\pi}{2}$
$\Rightarrow\sin^{-1}\text{x}=\frac{\pi}{6}$
$\Rightarrow\text{x}=\sin\frac{\pi}{6}=\frac{1}{2}$

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 "2 Marks Questions" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate:
$\text{cosec}\Big\{\cot^{-1}\Big(-\frac{12}{5}\Big)\Big\}$

$\text{If y}=\begin{vmatrix}\text{f(x)} & \text{g(x)} & \text{h(x)} \\ \text{l} & \text{m} & \text{n} \\ \text{a} & \text{b} & \text{c} \end{vmatrix},\ \text{prove that}\frac{\text{dy}}{\text{dx}}= \begin{vmatrix}\text{f(x)} & \text{g'(x)} & \text{h'(x)} \\ \text{l} & \text{m} & \text{n} \\ \text{a} & \text{b} & \text{c}\end{vmatrix}$

Find $\frac{{dy}}{{dx}},$ if $y = {\tan ^{ - 1}}\left( {\frac{{3x - {x^3}}}{{1 - 3{x^2}}}} \right), - \frac{1}{{\sqrt 3 }} < x < \frac{1}{{\sqrt 3 }}$

If $\text{y}=1-\text{x}+\frac{\text{x}^2}{2!}-\frac{\text{x}^3}{3!}+\frac{\text{x}^4}{4!}+...\infty$ then write $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ in terms of y.

A random variable has the following probability distribution:

$X = X_i$	$1$	$2$	$3$	$4$
$P(X = X_i)$	$k$	$2k$	$3k$	$4k$

Write the value of $\text{P}(\text{X}\geq3).$

Show that the function f defined by f(x) = |1 – x + | x | |, where x is any real number, is a continuous function.

Evaluate the following integrals:
$\int\cos^{-1}(\sin\text{x})\text{dx}$

Evaluate:
$\cot\Big(\sin^{-1}\frac{3}{4}+\sec^{-1}\frac{4}{3}\Big)$

Give example of matrices:
A, B and C such that AB = AC but B ≠ C, A ≠ 0

If two events A and B are such that $\text{P}(\overline{\text{A}})=0.3,\text{P(B)}=0.4$ and $\text{P}(\text{A}\cap\overline{\text{B}})=0.5$ find $\text{P}\Big(\frac{\text{B}}{\overline{\text{A}}\cap\overline{\text{B}}}\Big).$