Problem:
In △ABC,cos(2A−B)+sin(A+B)=2 and AB=4. What is BC ?
Answer Choices:
A. 2
B. 3
C. 2
D. 22
E. 23 Solution:
The maximum value for cosx and sinx is 1 ; hence cos(2A−B)= 1 and sin(A+B)=1. Therefore 2A−B=0∘ and A+B=90∘, and solving gives A=30∘ and B=60∘. Hence △ABC is a 30−60−90∘ right triangle and BC=2.