Question

IF TAN [A+B] = ROOT 3 AND TAN [A-B] =1/ROOT 3 THEN FIND THE VALUE OF A AND B

FASTEST WILL BE MARKED AS BRAINLIEST .

Answer 1

tan(a+b) = root3
tan(a-b)= 1/root3

We know tan 60 = root 3 and tan 30 = 1/root3

So, a+b = 60, a-b = 30

Adding the two gives

a+a+b-b=60+30
2a=90
a = 45
a+b=60
45+b=60
b=15

Answer 2

GIVEN THAT
tan[A+B]=√3

BUT WE KNOW THAT
TAN 60 DEGREE=√3

THUS

TAN (A+B)= TAN 60 DEGREE

A+B=60 DEGREE..............(1)


TAN [A-B]=1/√3

BUT WE KNOW THAT

TAN 30 DEGREE=1/√3

THUS

TAN (A-B)= TAN 30 DEGREE

A-B= 30 DEGREE...............(2)


OUR EQUATION ARE

A+B=60 DEGREE..............(1)
A-B= 30 DEGREE...............(2)


ADDING (1) AND (2)

A+B+A-B=60 DEGREE+ 30 DEGREE

2A=90 DEGREE

A=90 DEGREE/2

then A=45 DEGREE

PUTTING THE VALE OF A=45 DEGREE IN EQUATION.........(1)


A+B= 60°
45°+B=60°
B=60°-45°
B=15°


HENCE A=45°,B=15°