Question

If sin(A + B) = 1 and cos(A - B)=1, 0° ≤ (A + B ) ≤ 90° and A is greater than B, then find the value of A and B.

Answer 1

Step-by-step explanation:

Given sin(A+B)=1

⇒sin(A+B)=sin90  

o

 (∵sin90  

o

=1)

⇒A+B=90  

o

 …………(1)

Again, cos(A−B)=  

3

​  

/2

⇒cos(A−B)=cos30  

o

 (∵cos30  

o

=  

3

​  

/2)

⇒A−B=30  

o

 …………(2)

Adding (1)+(2)

A+B+A−B=90  

o

+30  

o

 

⇒2A=120  

o

 

⇒A=120/2

⇒A=60  

o

 

Putting A=60  

o

 in equation-(2) we get

A−B=30  

o

 

⇒60  

o

−B=30  

o

 

⇒60  

o

−30  

o

=B

⇒B=30  

o

 

∴A=60  

o

;B=30  

o

.

Answer 2

Step-by-step explanation:

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