Question

If sin (A-B)= 1/2, tan (A+B)=root3, then prove that angleA=45°.​

Answer 1

Step-by-step explanation:

Solution:

sin(A-B)=1/2

or,sin(A-B)=sin30°

or,A-B=30°

or,B=A-30°...........(i)

tan(A+B)=√3

or,tan(A+B)=tan60°

or,A+B=60°..........(ii)

Now,putting the value of A from eqn (i)

or,A+A-30°=60

or,2A=60°+30°

or,A=90°/2

Therefore,A=45°proved

Answer 2

angle A = 45°

Step-by-step explanation:

Since we have given that

$\sin (A-B)=\dfrac{1}{2}\\\\\sin (A-B)=\sin 30^\circ\\\\A-B=30^\circ--------------(1)$

Now,

$\tan(A+B)=\sqrt{3}\\\\\tan (A+B)=\tan 60^\circ\\\\A+B=60^\circ-------------(2)$

Using Eq(1) and (2), we get that

$A-B=30^\circ\\\\A+B=60^\circ\\\\----------------------------\\\\2A=90^\circ\\\\A=45^\circ\\\\B=60-45=15^\circ$

Hence, angle A = 45°

# learn more:

If sin A= root3/2 & cos B= root3/2, find the value of: tan A - tan B/1+tan A tan B.

https://brainly.in/question/37045