Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions5 Marks
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 "Solve the Following Question.(5 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

Solve the following system of equations by matrix method:
2x + y + z = 2
x + 3y − z = 5
3x + y − 2z = 6
→
If $\text{A}=\begin{bmatrix}1&2&2\\2&1&2\\2&2&1\end{bmatrix},$ then prove that $A^2 - 4A - 5I = 0.$
→
Find the angle between the pairs of lines with direction ratios proportional to
$2, 2, -2$ and $4, 1, 8$
→
If the median to the base of a triangle is perpendicular to the base, then triangle is isosceles.
→
Solve the follwing system of equations by matrix method:
$3x + 4y - 5 = 0$
$x - y + 3 = 0$
→
$\int\frac{2-3\text{x}}{\sqrt{1+3\text{x}}}\text{dx}$
→
Find the area of the region in the first quadrant bounded by the circle $x^2+y^2=4$ and the

X-axis and the line x = y√3.

→
Find the equations of tangents and normals to the curve at the point on it.

$2 x y+\pi \sin y=2 \pi$ at $\left(1, \frac{\pi}{2}\right)$

→
Solve the following differential equation:
$\frac{\text{dy}}{\text{dx}}+\text{y}=\cos\text{x}$
→
Differentiate the following functions with respect to x:
$\frac{\text{e}^{2\text{x}}+\text{e}^{-2\text{x}}}{\text{e}^{2\text{x}}-\text{e}^{-2\text{x}}}$
→