Consider the following statements I. `sin | x | + cos | x |` is always positive. II. `sin (x^2) + cos (x^2)` is always positive.

Options

A. 1 only
B. 2 only
C. Both 1 and 4
D. Neither 1 nor 4

Answer

D

Explanation

Statement 1 : `f_(1)(x)=sin|x|+cos|x|`, the value of `|sinx| and |cosx|` depends on its angles . `sin|x|+cos|x|` is not always positive.
Statement 2 : `f_(2)(x)=sin(x^(2))=cos(x^(2))` , the value of `x^(2)`
between any value which lies in the interval `(pi,(3pi)/(2))`,
then value of `f_(2)(x)=sin(x^(2))+cos(x^(2))` is always negative.