Question

if cos (x-y) = 1/2 and sin (x+y) =1/2 then what is the largest value of x

Answer 1

Cos (A+B) = 0.

But we know that Cos 90 = 0.

A+B = 90. 
A = 90 - B. ​---- (1)

Sin (A-B) = Cos [90-(A-B)]
Sin (A-B) = Cos [90-A+B]

Substituting A value from (1),

Sin (A-B) = Cos [90-(90-B)+B]
Sin (A-B) = Cos (2B).