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

Consider the following statements I. sin |x| + cos |x| is always positive II. sin(x^2) + cos (x^2) is always positive Which of the above statement is/are correct?

cos 2x + 2cos x is always :-

If x is real, prove that the quadratic expression (i) (x-2)(x+3)+7 is always positive. (ii) 4x-3x^(2)-2 is always negative.

(sin x + cos x)^2 + (sin x - cos x)^2

Show that the following funtion are everywhere continuous , (i) sin x+ cos x (ii) sin ^2x (iii) |cos x|

For real values of 'x' , Which of the following is/are always positive? (a) sin(cosx) (b) sin(sinx)

For real values of 'x' , Which of the following is/are always positive? (a) sin(cosx) (b) sin(sinx)

Consider the equation 5 sin^2 x + 3 sin x cos x - 3 cos^2 x =2 .......... (i) sin^2 x - cos 2 x =2-sin 2 x ........... (ii) The number of solutions common to (i) and (ii) is

Consider the equation 5 sin^2 x + 3 sin x cos x - 3 cos^2 x =2 .......... (i) sin^2 x - cos 2 x =2-sin 2 x ........... (ii) The number of solutions common to (i) and (ii) is