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if cos(a-b)=1/2 and sin(a+b)=1/2 find smallest positive values of a and b and also their most general values

if cos(a-b)=1/2 and sin(a+b)=1/2 find smallest positive values of a and b and also their most general values

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2 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
7 years ago
cos(a-b)=1/2, a-b=2nPi+Pi/3
sin(a+b)=1/2, a+b=2nPi+Pi/6
a=2nPi+1/2(Pi/3+Pi/6), a=2nPi+Pi/4
b=2nPi+1/2(Pi/6-Pi/3), b=2nPi-Pi/6
smallest value for n=0,
a=Pi/4
b=-Pi/6

sher mohammad
b.tech, iit delhi


NIKHIL JHA
41 Points
7 years ago
SINCE WE NEED TO FIND THE SMALLEST POSSIBLE VALUE FOR a & b both a & b should lie in first quadrant and SIN(a+b)=1/2 ===>>> SIN(a+b)=SIN (pi/6)=====>> a+b=pi/6.........(1) COS(a-b)=1/2 ===>>>COS(a+b)=COS(pi/3)=====>> a-b=pi3..........(2) solve for a and b===>> a=pi/4 b=pi/6

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