If f(x) = sin [π2] x + sin [-π2] x, where [x] denotes the greatest i

1.	If f(x) = sin [π2] x + sin [-π2] x, where [x] denotes the greatest integer less than or equal to x, then A. f (π/2) = 1 B. f(π) = 2 C. f (π/4) = - 1 D. None of these
Answer» π² ≈ 9.8596 [π²] = 9 and [-π²] = -10 Now, f(x) = sin[π²] x + sin[-π²]x = sin 9x - sin 10x Now, Checking values of f(x) at given points.. f(\(\frac{\pi}{2}\)) = sin 9(\(\frac{\pi}{2}\)) - sin 10(\(\frac{\pi}{2}\)) = 1-0 = 1 Option A is correct.. f(π) = sin 9π - sin 10π = 0 - 0 = 0 f(\(\frac{\pi}{4}\)) = sin 9(\(\frac{\pi}{4}\)) - sin 10(\(\frac{\pi}{4}\)) = \(\frac{1}{\sqrt 2}\) - 1 Option B & C are incorrect..

If f(x) = sin [π2] x + sin [-π2] x, where [x] denotes the greatest integer less than or equal to x, then A. f (π/2) = 1 B. f(π) = 2 C. f (π/4) = - 1 D. None of these

Answer»

π² ≈ 9.8596

[π²] = 9 and

[-π²] = -10

Now,

f(x) = sin[π²] x + sin[-π²]x

= sin 9x - sin 10x

Now,

Checking values of f(x) at given points..

f(\(\frac{\pi}{2}\)) = sin 9(\(\frac{\pi}{2}\)) - sin 10(\(\frac{\pi}{2}\))

= 1-0

= 1

Option A is correct..

f(π) = sin 9π - sin 10π

= 0 - 0

= 0

f(\(\frac{\pi}{4}\)) = sin 9(\(\frac{\pi}{4}\)) - sin 10(\(\frac{\pi}{4}\))

= \(\frac{1}{\sqrt 2}\) - 1

Option B & C are incorrect..