Question

If sin (A + B) = cos(A - B) = 1, then a *B=0° (b) A= B = 45° c) A = 60°, B = 30° (d) A = 90° B = 60°​

Answer 1

Answer:

A=45° and B=45°

Step-by-step explanation:

sin(A+B)=cos(A−B)

⇒ sin(A+B)=sin[ 90° − (A− B) ]  

⇒A+B=90° −(A−B)                               -----(i)

⇒2A=90°

⇒A=45° so now,

If B=1 then sin(45 + B) = 1 = sin(90°)

⇒45° + B = 90°

so B = 45°

Verification:

sin(45+45) = sin90° = 1 = cos(45-45) = cos0° = 1

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Answer 2

Answer:

Option (B)  A = B = 45°

Step-by-step explanation:

Finding value of A

$sin ( A+B) = cos ( A-B)\\cos ( 90 - (A+B)) = cos (A-B)\\90 - A - B = A-B\\90 - A = A\\2A = 90\\A = 45$

Finding Value of B

$cos ( A-B) = 1\\cos (0) = 1\\hence, A - B = 0\\\\A - B = 0\\45 - B = 0\\B = 45$

Finally, the correct option is (B) A = B = 45°