Question

If sin (A+B) = 1 and sin (A-B) = 1/2, 0<A +B< 90° and A >B, then find
A and B.
tan A​

Answer 1

We know that

Sin (A+B)=1

A+B=90 equation 1

Sin(A-B)=1\2

A-B=30 equation 2

Solving eq.1and2

A+B=90

A=90-B eq.3

Put the value of A in eq.2

90-B-B=30

-2B =30-90

-2B=-60

B=30

Put the value of B in eq.3

A=90-30

A=60

Hence prooved

Make it brainliest answer

Answer 2

Step-by-step explanation:

sin(A+B) = 1

→ sin(A+B) =sin90°

→ A + B =90°..............(i)

sin(A-B) = 1/2

→ sin(A-B) = sin30°

→ A-B =30°.................(ii)

•By elimination:-

A+B =90°

A-B = 30°

___________

2A = 120°

→ A = 60°

• Put the value of A = 60° in the (i) equation:-

A+B = 90°

→ 60° +B = 90°

→ B = 90°-60°

→ B = 30°

tanA

= tan60°[ put A = 60° ]

= ✓3

★Answer:-

• A = 60°
• B= 30°
• tanA = ✓3