Show that ^ -1 (2x 1-x^2 )=2 ^ -1 x. - Vidyadip

Question

Show that $\sin^{-1}\Big(2\text{x}\sqrt{1-\text{x}^2}\Big)=2\sin^{-1}\text{x}.$

✓

Answer

We have $\text{L.H.S}=\sin^{-1}\Big(2\text{x}\sqrt{1-\text{x}^2}\Big)$Putting $\text{x}=\sin\text{a},$ we get
$=\sin^{-1}\Big(2\sin\text{a}\sqrt{1-\sin^2\text{a}}\Big)$
$=\sin^{-1}(2\sin\text{a}\cos\text{a})$
$=\sin^{-1}(\sin2\text{a})$
$=2\text{a}$
$=2\sin^{-1}\text{a}$ $(\because\ \text{x}=\sin\text{a})$

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 Trigonometric Functions→Inverse Trigonometric Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{A}=\begin{pmatrix}3&5\\7&9 \end{pmatrix}$ is written as A = P + Q, where as A = P + Q, where P is a symmetric matrix and Qis skew symmetric matrix, then write the matrix P.

Examine the consistency of the system of equation x + 2y = 2; 2x + 3y = 3

Evaluate the following integrals:
$\int\frac{(\sin^{-1}\text{x})^3}{\sqrt{1-\text{x}^2}}=\text{dx}$

Evaluate the following integrals:$\int\text{e}^{\text{x}}\Big(\frac{\text{x}-1}{2\text{x}^2}\Big)\text{dx}$

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.

What is the value of the determinant $\begin{vmatrix}0&2&0\\2&3&4\\4&5&6\end{vmatrix}?$

Transitive but neither reflexive nor symmetric.

If $\begin{bmatrix}1&0&0\\0&\text{y}&0\\0&0&1\end{bmatrix}\begin{bmatrix}\text{x}\\-1\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\0\\1\end{bmatrix}$, find x, y and z.

What are the direction cosines of X-axis?

If $f : R \rightarrow R$ defined by $f(x) = 3x - 4$ is invertible, then write $f^{-1}(x).$