Solve: 2 ^ -1 -x =0 - Vidyadip

Question

Solve: $\cos\Big\{2\sin^{-1}\{-\text{x}\}\Big\}=0$

✓

Answer

$0=\cos\Big\{2\sin^{-1}\{-\text{x}\}\Big\}$
$0=\cos\Big(\sin^{-1}\Big(-2\times\sqrt{1-\text{x}^2}\Big)\Big)\\.....\Big[2\sin^{-1}\text{x}=\sin^{-1}\Big(2\times\sqrt{1-\text{x}^2}\Big)\Big ]$
$$$0=\cos\Big(\cos^{-1}\sqrt{1-\big(4\text{x}^2-4\text{x}^4}\big)\Big)\\.....\Big[\sin^{-1}\text{x}=\cos^{-1}\sqrt{1-\text{x}^2}\Big]$
$$$0=\sqrt{1-\big(4\text{x}^2-4\text{x}^4\big)}$
$0=1-\big(4\text{x}^2-4\text{x}^4\big)$
$4\text{x}^4-4\text{x}^2+1=0$
$4\text{x}^4-2\text{x}^2-2\text{x}^2+1=0$
$2\text{x}^2\big(2\text{x}^2-1\big)-1\big(2\text{x}^2-1\big)=0$
$\big(2\text{x}^2-1\big)^2=0$
$2\text{x}^2-1=0$
$\text{x}=\pm\frac{1}{\sqrt2}$

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 "3 Marks Question" 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

An urn contain 5 red and 2 black balls. Two balls rendomly selected. Let X represent the number of black ball. What are the possible values of X. Is X a random variable?

Find specific solution of differential equation $\left(1+x^2\right) \frac{d y}{d x}+2 x y=\frac{1}{1+x^2}$ at $y=2, x=1$.

Verify that $\text{y}=4\sin3\text{x}$ is a solution of the differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}+9\text{y}=0.$

Let * be a binary operation on Q - {-1} defined by a * b = a + b + ab for all a, b ∈ Q - {-1}. Then,
Show that every element of Q − {−1} is invertible. Also, find the inverse of an arbitrary element.

Find the mean and standard deviation of the following probability distributions:

$\text{x}_\text{i}$	$0$	$1$	$2$	$3$	$4$	$5$
$\text{p}_\text{i}$	$\frac{1}{6}$	$\frac{5}{18}$	$\frac{2}{9}$	$\frac{1}{6}$	$\frac{1}{9}$	$\frac{1}{18}$

Find the equation of a plane which bisects perpendicularly the line joining the points A(2, 3, 4) and B(4, 5, 8) at right angles.

Evaluate the following integrals:
$\int_{4}^\limits{12}\text{x}(\text{x}-4)^{\frac{1}{3}}\text{dx}$

If $\text{A}=\begin{bmatrix}\sin\alpha&\cos\alpha\\-\cos\alpha&\sin\alpha\end{bmatrix},$ verify that $A^TA = I_2$.

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b ): b = a +1} is reflexive, symmetric or transitive.

If $\text{x}=\text{a}(\cos2\text{t}+2\text{t}\sin2\text{t})\ \text{and}\ \text{y}=\text{a}(\sin2\text{t}-2\text{t}\cos2\text{t}),$ then find $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$