Question

(i) tan (A + B) = 73 and tan (A-B) = 1/
V3, where A B and (A+B) is acute,
then A = ?​

Answer 1

Answer:

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°