Question

If sin(A+B) = root3/2, tan (A - B) =1/root3 , find A and B.​

Answer 1

Answer:

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Step-by-step explanation:

sin(A+B)=√3/2

A+B=60°

Hence, A= 60-B

tan(A-B)=1/√3

A-B=30°

B-(60-B)=30

2B-60=30

2B=90

Hence B=45°

A= 60-45

Hence, A= 15°

Answer 2

Answer:

A=45 and B=15

Step-by-step explanation:

here,

=sin(A+B)=√3/2

=sin(A+B)=sin60°   ------------------------------------{∵sin60°=√3/2}

=A+B=60         ---------------------{1}

and,

=tan(A-B)=1/√3

=tan(A-B)=tan30°      --------------------------------------∵{tan30°=1/√3}

=A-B=30     ------------------------------------{2}

by adding equation {1} and {2},we get,

2A=90

A=45

applying A=45 in {1},

{45}+B=60

B=60-45

B=15

∴A=45 and B=15