Question

Consider, sin A = 4/5 and cos B= 5/13, where 0 < A and B < π/2. Based on the above information answer the questions from 31 to 35. 31. The value of cos A + sin B is *

Answer 1

Answer:

A=54,cosB=135

sinA=54, A ϵ (π/2,π)

⟹cosA=25−163=5−3

cosB=135,B ϵ (3π/2,2π)

So, sinB=13−12

(1)  sin(A+B)=sinAcosB+cosAsinB=(54)(135)+(5−3)(13−12)=6556

(2)  cos(A−B)=cosAcosB+sinAsinB=(5−3)(135)+(