but range of LHS is -pi to pi and range of RHS is -pi/2 to pi/2.so this equation will be true if

lies between -pi/2 to pi/2. This happens if cos(A+B)>=0 as its >=0 between -pi/2 to pi/2

so

or

If x,y>=0 or x,y <= on squaring there will be no change is sign therfor on squaring we get

also if xy<0 but

on squaring there will be again no change of equality sign and we will get

but if xy<0 and

on squaring there will be change of equality sign and we will get

so finally we get

if

1)

and

a)x,y>=0

b)x,y<=0

c)xy<0 and

2)

if

xy<0 and

but all the books that I have read say nothing about

and

. Are they not necesrary???