We, are given information that both sin(x) and cos(y) lie in second quadrant.
By that we can say that sin will be positive and cos will be negative.
sin(x)=3/5
cos(x)=(1 – sin2(x))1/2
cos(x)=+(or) – 4/5
Since,(x) is in 2nd quadrant, cos(x) will – 4/5
cos(x – y) = cos(x)cos(y) + sin(x)sin(y)
Similarly, sin(y)=5/13.
By, applying the above formula we get:
cos(x-y) = (-)4/5*(-)12/13 + 3/5*5/13
= 63/65
For, the second part we would be using the given below formula:
tan(x+y) = (tan(x) + tan(y)) ÷ (1 – tan(x)tan(y))
tan(x)=3/5 & tan(y)=5/12
tan(x+y) = [3/5 + 5/12]÷[1 – 3/5×5/12]
= 61/45
