Solution 4.3:7b

From Förberedande kurs i matematik 1

Using the addition formula, we rewrite sin(x+y) as

sin(x+y)=sinxcosy+cosxsiny.

If we use the same solution procedure as in exercise a, we use the Pythagorean identity cos2v+sin2v=1 to express the unknown factors sinx and siny in terms of cosx and cosy,

sinxsiny=1−cos2x=1−522=1−425=521=1−cos2y=1−532=1−925=54.

The angles x and y lie in the first quadrant and both sinx and siny are therefore positive, i.e.

sinx=521andsiny=54.

Thus, the answer is

sin(x+y)=52153+5254=25321+8.