Question

find a and b
Sin (A+B)
=Cos (A-B )=root 3 /2​

Answer 1

Given sin(A+B)=1

⇒sin(A+B)=sin90o (∵sin90o=1)

⇒A+B=90o …………(1)

Again, cos(A−B)=3/2

⇒cos(A−B)=cos30o (∵cos30o=3/2)

⇒A−B=30o …………(2)

Adding (1)+(2)

A+B+A−B=90o+30o

⇒2A=120o

⇒A=120/2

⇒A=60o

Putting A=60o in equation-(2) we get

A−B=30o

⇒60o−B=30o

⇒60o−30o=B

⇒B=30o

∴A=60o;B=30o.

Answer 2

Answer:

a=60° b=30°

Explanation:

Given sin(A+B)=1

⇒sin(A+B)=sin90 °(∵sin90 °=1)

⇒A+B=90° …………(1)

Again, cos(A−B)= 3/2

⇒cos(A−B)=cos30 ° (∵cos30°=3 /2)

⇒A−B=30°…………(2)

Adding (1)+(2)

A+B+A−B=90°+30°

⇒2A=120°

⇒A=120/2

⇒A=60 °

Putting A=60° in equation (2) we get

= A−B=30°

⇒60°−B=30°

⇒60° −30° =B

⇒B=30

∴A=60°

B=30°