Solve: ( ^ -1 1 5 + ^ -1 x )=1 - Vidyadip

Question

Solve:
$\sin\Big(\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}\Big)=1$

✓

Answer

$\sin\Big(\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}\Big)=1$
$\Rightarrow\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}=\sin^{-1}1$
$\Rightarrow\sin^{-1}\frac{1}{5}+\cos^{-1}\text{x}=\frac{\pi}{2}$
$\Rightarrow\sin^{-1}\frac{1}{5}=\frac{\pi}{2}-\cos^{-1}\text{x}$
$\Rightarrow\sin^{-1}\frac{1}{5}=\sin^{-1}\text{x}$ $\Big[\because\ \sin^{-1}\text{x}=\frac{\pi}{2}-\cos^{-1}\text{x}\Big]$
$\Rightarrow\text{x}=\frac{1}{5}$

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 "Solve the Following Question.(3 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find a vector of magnitude 49, which is perpendicular to both the vectors $2\hat{\text{i}}+3\hat{\text{j}}+6\hat{\text{k}}$ and $3\hat{\text{i}}-6\hat{\text{j}}+2\hat{\text{k}}.$

If $4\sin^{-1}\text{x}+\cos^{-1}\text{x}=\pi,$ then what is the value of x?

If $y=f(u)$ is a differentiable function of $u$ and $u=g(x)$ is a differentlable function of $x$, then prove that $y=f g(x)$ is a differentiable function of $x$ and $\frac{d y}{d x}=\frac{d y}{d u}. \frac{d u}{d x} \quad$

Diffrentiate the following w. r. t. x.

$\cos ^{-1}\left(\frac{3 \cos \left(e^x\right)+2 \sin \left(e^x\right)}{\sqrt{13}}\right)$

Find the values of $x$ for which $f ( x )=\frac{ x }{x^2+1}$ is
(a) strictly increasing (b) strictly decreasing.

Evaluate : $\int x \cdot \sin ^{-1} x \cdot d x$

Show that the points $(1,-1,3)$ and $(3,4,3)$ are equidistant from the plane $5 x+2 y-7 z+8=0$.

Diffrentiate the following w. r. t. x.

$\tan ^{-1}\left(\frac{2 \sqrt{x}}{1+3 x}\right)$

$\int \frac{1}{4 x^2-20 x+17} d x$

Find $\frac{d y}{d x}$ if

$x=\sqrt{a^2+m^2}, y=\log \left(a^2+m^2\right)$