Question

If $f\left(x\right)=x^3-2x^2+3x-5$ , then $f\left[\sin \right(\frac{5\pi }{2}\left)\right]+f\left[\sin \right(\frac{3\pi }{2}\left)\right]=$

• A. $10$
• B. $-10$
• C. $14$
• D. $-14$

Answer 1

The correct option is D $-14$

$sin\left(\frac{5\pi }{2}\right)$
$=sin(2\pi +\frac{\pi }{2})$
$=sin\left(\frac{\pi }{2}\right)$
$=1$ ....(i)
And
$sin\left(\frac{3\pi }{2}\right)$
$=sin(\pi +\frac{\pi }{2})$
$=-sin\left(\frac{\pi }{2}\right)$
$=-1$ ...(ii)
Then
$f\left(1\right)+f(-1)$
$=[1-2+3-5]+[-1-2-3-5]$
$=[4-7]+[-11]$
$=-11-3=-14$