Grade 11Trigonometry
If cosx+cosy-cos(x+y)=3/2 then find the value of SinxSiny where x>0, y
If cosx+cosy-cos(x+y)=3/2 then find the value of SinxSiny where x>0, y
2 Answers
noogler
cosx+cosy-cos(x+y)=3/2 is true if x=y=60o
cos60o+cos60o-cos120o=1/2+1/2-(-1/2)=3/2
SinxSiny=sin60o sin60o=3/4
sinx siny=3/4
approve if it is r8 and useful to u..........
Lab Bhattacharjee
⟹22cos(x+y)/2cos(x-y)/2-[2cos^2(x+y)/2-1]=3/2
implies 4cos^2(x+y)/2-4cos(x+y)/2cos(x-y)/2+1=0
As cos(x+y)/2 is real, the discriminant (4cos(x-y)/2)^2-4^2=-16sin^2(x-y)/2 must be >=0
So, sin^2(x-y)/2=0 implies sin(x-y)/2=0 implies(x-y)/2=n pi, x-y=2n pi where n is an integer
So, (2cos(x+y)/2-1)^2=0, cos(x+y)/2=1/2=cos pi/3 implies (x+y)/2=2m pi +/- pi/3 implies x+y=4n pi +/- 2pi/3
Solve for x,y
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