Let f(x) = sin x|sin x + sin 3x| , then a) f(x) greater than equal to 0, - Maths - Relations and Functions

Question

Let f(x) = sin x|sin x + sin 3x| , then
a) f(x) greater than equal to 0, when x is greater than equal to
0

b) f(x) is less than equal to 0 for all real values of x

c) f(x) is greater than equal to 0 for all real x

d) f(x) is less than equal to 0, when x is less than equal to 0

Anuradha Sharma · Accepted Answer

We have,fx = sin xsin x + sin 3x=sin xsin x + 3 sin x - 4sin3x=sin
x4 sin x - 4 sin3x=4 sin2x1 - sin2x= 4 sin2 x cos2x=2 sin x cos
x2=sin 2x2Now, sin 2x2 ⩾0 as it is a square quantity ∀
x∈R Hence, fx ⩾0 ∀ x∈R

Hence option (c) is correct

Let f(x) = sin x|sin x + sin 3x| , thena) . f(x) greater than equal to 0, when x is greater than equal to 0 b). f(x) is less than equal to 0 for all real values of x. c). f(x) is greater than equal to 0 for all real x. d). f(x) is less than equal to 0, when x is less than equal to 0.

Let f(x) = sin x|sin x + sin 3x| , then
a) . f(x) greater than equal to 0, when x is greater than equal to 0

b). f(x) is less than equal to 0 for all real values of x.

c). f(x) is greater than equal to 0 for all real x.

d). f(x) is less than equal to 0, when x is less than equal to 0.