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

Find the principal values of the following : sin^(-1)["sin"(2pi)/3]

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.

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"):}

Give converse and contrapositive of following statement: If x is negative x^(2) is positive.

The roots of a plant are A) positive phototropic, but negative geotropic B) negative geotropic, but negative phototropic C) negative phototropic, but positive hydrotropic D) negative hydrotropic, but positive phototropic

The principal value of arg (z) , where z=1+cos((8pi)/5)+i sin((8pi)/5) (where, i=sqrt-1) is given by

A particle starts from point x = (-sqrt(3))/(2)A and move towards negative extreme as shown, (a) Find the equation of the SHM (b) Find the time taken by the particle to go directly from its initial position to negative extreme. (c) Find the time taken by the particle to reach at mean position.

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

Let n be a positive integer such that sin(pi/(2n))+cos(pi/(2n))=(sqrt(n))/2 Then

In a mixture of A and B components show negative deviation when