If sin(A+B)=1,cos(A−B)=1, 0∘≤A+B≤90∘, Find A and B.
If A+B lies in this range 0∘<A+B≤90∘
sin(A+B)=1 only when A+B=90∘ ............ (1)
cos(A−B)=1, only when A−B=0∘ ............ (2)
Lets add eq (1) and eq (2),
A+B+A−B=90∘+0∘
⇒2A=90∘
⇒A=45∘
From(1)
45∘+B=90∘
⇒B=45∘
Hence, option A is correct.