Question

if sin(A-B)=1/2 and A+B=90 find 'A'and 'B'​

Answer 1

cos(A+B) = 1/2

⇒cos (A+B) = cos(60)  (as 0<A+B<90)

⇒A+B = 60

sin(A-B) = 1/2

⇒sin(A-B) = sin(30) or sin (150)

⇒A-B = 30 or 150

Case:1

A - B = 30

A + B = 60

Solving we get, A = 45 and B = 15

A>B is satisfied.

Case:2

A - B = 150

A + B = 60

Solving, we get A = 105, B = -45

A>B is satisfied.

So the value of A can be 45 or 105.

Answer 2

$\huge\bold{Question:-}$

• If sin (A - B) = 1/2 and A + B = 90°
• Find A and B

$\huge\bold{Solution:-}$

Given

Sin (A - B ) = 1/2

We know that Sin 30°= 1/2

So A - B = 30°______(1)

A = B + 30°

B = A - 30°________(2)

And also given A + B = 90°_________(3)

Solving (1) and (3)

A - B = 30°

(+) A + B = 90°

____________

2A = 120°

____________

A = 120/2

=> A = 60°

So, from (2)

B = 60° - 30°

= 30°

$\huge\bold{Final Answer:-}$

• A = 60°
• B = 30°

Hope this is helpful