Trignometry question cos x. sin y=1 & 0<=x<=3pie

Active member

if 0<=x<=3pie , 0<=y<=3pie and cos x. sin y=1 the possible number.of ordered pair of (x,y) is
a)4
b)8
c)6
d)12

Active member

hint:
-1<=cos x<=1, -1<=siny<=1. So, cos x. siny<=1. Equality occurs if cosx = 1 and siny =1 or cosx = -1 and siny = -1. From this obtain the possible pairs

Active member

other method:-
SOLNS EXIST WEN cosx =1 and cosecy=1 ie x=0,2pi y=pi/2,5pi/2 =>4solns

and

wen

cosx =-1 and cosecy=-1 ie x=pi,3pi y=3pi/2 =>2 solns

in total 6 ans