Question

If sin (A – B) = 1 and cos(A + B) = 1, then the value of A and B, respectively are

Answer 1

Answer:

Sin(A-B) = 1

Cos(90 - A+B) = 1

But cos (A+B) = 1

SO,

Cos (90-A+B) = Cos (A+B)

90 - A+B= A+B

2A = 90

A = 45

Answer 2

The value of A is 45° and value of B is -45°

Step-by-step explanation:

Given : sin(A-B)= 1 and cos(A+B)=1

To find: The value of A and B

As given

sin(A-B)=1

⇒sin(A-B)=sin 90°                   (∵ sin 90°=1)

⇒A-B= 90° ------(i)                    (∵ if sin x= sin y then x=y)

similarly

  cos(A+B)=1

⇒  cos (A+B)= cos 0°                 (∵ cos 0°= 1)

⇒  A+B=0°                                  (∵ cos x= cos y then x=y)

⇒  A=-B

substituting the value in (i) we get

  -B-B=90°

⇒ -2B= 90°

⇒  B= -45°

And A= - B = -(-45°)=45°

Hence the value of A is 45° and value of B is -45°

# Learn more

If sin (a+b)=1 and cos (a-b)=1 find the value of A and B

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