Show that if a and b are real, the principal value of arg a is 0 or π according as a is positive or negative and that of bi is `pi/2 or -pi/2` according as b is positive or negative.

The function f(x) = sin x-x cos x is: (A).maximum or minimum for all integral multiple of pi (B) maximum if x is an odd positive or even negative integral multiple of pi (C) minimum if x is an even positive or odd negative integral multiple of pi (D) None of these

If a ,b ,c are sides of a scalene triangle, then value of |[a, b, c] ,[b, c, a] ,[c, a, b]| is positive (b) negative non-positive (d) non-negative

Depending on in which quadrant an angle theta lies, functions costheta and sintheta may be positive or negative. In the second column of the given lable are specified whether these functions are positive or negative and in the first column are specified quadrants. {:("Column-I","Column-II"),((A)" First",(P)sintheta" is positive"),((B)" Second",(Q)sintheta" is negative"),((C)" Third",(R)costheta" is negative"),((D)" Fourth",(S)tantheta" and "sintheta"both are negative"),(,(T)sectheta" is negative and "sintheta" is positive"):}

The value of xyz is 55 or (343)/(55) according as the series a,x,y,z,b is an AP or HP. Find the values of a and b given that they are positive integers.

The principal value of the amplitude of (1+i) is A. pi B. pi/(12) C. pi/4 D. (3pi)/4

Find interval of values of ' a ' for which one root of equation x^2+a^2(x+1)+(a-2)=0 is negative and the other root is positive

The least numerical value, either positive or negative of angle theta is called principal value of the inverse trigonometric function.

In what quadrant does an angle lie if (a) its sine is positive and its cosine is negative ? (b) Its tangent positive and its sine is negative ? (c ) its cosine is positive and its tangent is negative ? (d) its sine is negative and its cosine is positive ?

A car goes A to B along the path with constant accelertion "a" as shown in figure. Student -1 infers that initial velocity is positive acceleration is negative and displacement is positive. Student-2 infers that initial velocity is negative. acceleration is positive and displacement is positive.

If a, b, c are positive and unequal, show that value of the determinant Delta=|a b c b c a c a b| is negative.