Question

If tan (A-B) =V3, and sin (A+B) =1, then find A and B​

Answer 1

Given,

tan(A-B)=root3

=>tan(A-B)=tan60°

=>A-B=60

=>A=60+B ---------- (i)

Also given,

sin(A+B)=1

=>sin(A+B)=sin90°

=>A+B=90

=>(60+B)+B=90 [from (i)]

=>2B=90-60

=>B=30/2

=>B=15° ---------- (ii)

Now,

(i)=>A=60+(15) [from (ii)]

=>A=75°

Answer 2

Answer:

Tan ( A - B ) = root 3

ie .. Tan 60 = root 3

so A - B = 60 -----------(1)

Sin ( A + B ) = 1

ie.. Sin 90 = 1

so A + B = 90-----------(2)

Adding 1 and 2

A - B + A + B = 60 + 90

2A = 150

A = 150 / 2 = 75

so A = 75

Substituting The value of A in equation ( 1 )

A - B = 60

75- B = 60

-B = 60 - 75 = - 15

B = 15

A = 75 and B = 15

hope it helps u mate ✌