Question

if sinA+B= 1 and sin A-B =1/2,0 = A +B =90 and A>B , then find A and B

Answer 1

Step-by-step explanation:

Given that... sin ( A + B ) = 1

But sin 90 = 1

therefore.... sin (A + B ) = sin 90

                         A + B = 90 .........(1)

Case 1

Sin ( A- B ) = 1/2            ( Sin 30 = 1/2 )

therefore... sin ( A - B ) = sin 30

                        A - B = 30.........(2)  

from 1 & 2

A + B + A - B = 90 + 30

2A = 120

A = 60

Therefore.. B = 30

Case 2

sin ( A- B ) = 0                  ( Sin 0 = 0 )

Sin ( A-B ) = Sin 0

A - B = 0

therefore.... A = B

Therefore A = B = 45

                   

Answer:   Case 1 -> A = 60 , B = 30

                 Case 2 -> A=B= 45

Answer 2

Answer:

Values of A and B are 60° and 30° respectively.

Step-by-step explanation:

Given,

   sin( A + B ) = 1

From trigonometric table, we know that the value of value of sin90° is 1,

So, substitute value of 1.

= >  sin( A + B ) = sin90°

= >  A + B = 30°        ...( i )

Also,

sin( A - B ) = 1 / 2

From trigonometric table, we know that the value of value of sin30° is 1,

So, substitute value of 1 / 2 .

= >  sin( A - B ) = sin30°

= >  A - B = 30°         ...( ii )

Now, adding ( i ) and ( ii ),

A + B = 90°

A - B = 30°

2A = 120°

= >  A = 120° / 2

= >  A = 60°

Substitute value of A in ( i ),

= >  A + B = 90°

= >  60° + B = 90°

= >  B = 90° - 60°

= >  B = 30°

Therefore , A = 60° and B = 30°