Question

if tan a + b equals to root 3 and 10 a minus b equals to 1 upon root 3 find the value of a and b

Answer 1

QUESTION :

if tan (a + b) equals to root 3 and tan(a - b) equals to 1 upon root 3 find the value of a and b

ANSWER :

GIVEN :

tan(a+b)=√3

tan(a-b)=1/√3

TO FIND :

a=?

b=?

SOLUTION :

tan(a+b)=√3

but tan60=√3

so a+b=60.......1

now

tan(a-b)=1/√3

but tan30=1/√3

a-b=30......2

so by elimination method adding 1 and 2

2a=60+30

a=45°

put a in 1

b=60-(45)

=15°

hence

(a,b)={45°,15°}

NOTE :

try to simplify the answer first

and don't use double angle formulae to make it more difficult

Also the question was incorrect

it should be tan(a-b)=1/√3

not 10a-b=1/√3