The number of pairs (x, y) satisfying the equations
The first equation can be written as
When x + y = 0, we have to reject x + y = 1 or –1 and solve it with x – y = 1 or x – y = –1 which give (1/2, –1/2) or (–1/2, 1/2) as the possible solutions. Again solving with x = 0 we get and solving with y = 0 we get as the other solutions. Thus we have six sets of solutions for x and y.
The number of values of x in the interval satisfy the equation is
The number of solutions of the pair of equations
in the interval is
If are the smallest +ive angles in ascending order of magnitude which have their sines equal to a +ive quantity then the value of
The equation possesses a solution if
The number of values of x in the interval satisfying the equation is
The number of solutions of the equation
If n be the number of solutions of the equation
, then n =
The values of x between 0 and which satisfy the equation
are in A.P. The common difference of the A.P.