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if tan(a- b)=1 and sec(a+b)=2/root 3 . find the smallest positive values of a and b and also their most general values

if tan(a- b)=1 and sec(a+b)=2/root 3 . find the 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
8 years ago
a-b=nPi+ Pi/4
1/cos(a+b)=sec(a+b)=2/root 3
cos(a+b)=root 3/2
a+b=2nPi+Pi/6
a=2nPi+1/2(Pi/4+Pi/6)
b=2nPi+1/2(Pi/6-Pi/4)
for n=0,
smallest value of a=1/2(Pi/4+Pi/6)
smallest value of b=1/2(Pi/6-Pi/4)

sher mohammad
b.tech, iit delhi
Santosh kumar Anakapalli
11 Points
5 years ago
tan(A-B) = 1 then A-B = 45 or 225 degrees
Sec(A+B) = 2/sqt3 then A+B either 30 or 330  degrees
then if take A-B = 45 and A+B = 330 then A= 187.5  degrees, B = 142.5  degrees.
 
Santosh Kumar Anakapalli
NIT Trichy

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