Question

10.已知锐角A，B满足sinA=√5/5，cosB=3√10/10,则A+B等于？

答案是多少，为什么？

Answer 1

cosA=√(1-sin²A)=2√5/5
sinB=√(1-sin²B)=√10/10
cos(A+B)
=cosAcosB-sinAsinB
=2√5/5 ×3√10/10-√5/5×√10/10
=√2/2
所以
A+B=π/4.