Question

$Letf\left(x\right)={sin}^{-1}sinx+{cos}^{-1}cosx,$ $g\left(x\right)=mxandh\left(x\right)=x$ are three functions. Now $g\left(x\right)$ divided area between $f\left(x\right),x=\pi$ and $y=0$ into two equal parts .
The value of m is :

• A. $\frac{1}{4}$
• B. $\frac{3}{4}$
• C. $\frac{5}{4}$
• D. $\frac{7}{4}$

Answer 1

Answer: (A)

$\frac{1}{4}$

The area formed by,

$f\left(x\right),x=\pi ,y=0$ is a right angled triangle.

when a right angles triangle is divided into 2 equal halves, we get, 2 more further parallelograms.

and as area of 2 triangles make up area of a parallelogram.

$\therefore m=\frac{1}{4}$