Question 951463
Given cos(x) = 1&#8260;9 with 0o < x < 90o, and cos(y) = 1&#8260;11 with 270o < y < 360o. Find cos(x + y).
***
cosx=1/9 (Q1)
sinx=&#8730;(1-cos(x)^2)=&#8730;(1-1/81)=&#8730;(80/81)=&#8730;80/9
cosy=1/11(Q4)
siny=-&#8730;(1-cos(y)^2)=-&#8730;(1-1/121)=-&#8730;(120/121)=-&#8730;120/11
..
cos(x+y)=cosxcosy-sinxsiny=1/9*1/11-&#8730;80/9*-&#8730;120/11=1/99+&#8730;9600/99=(1+&#8730;9600)/99
Check:
Cosx=1/9
x&#8776;83.62&#730;
cosy=1/11
y&#8776;275.22&#730;
x+y&#8776;358.84&#730;
cos(x+y)&#8776;cos(358.54)&#8776;0.9997
exact value as computed=(1+&#8730;9600)/99&#8776;0.9997