Question #bfb94

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Answer 1 · 2017-12-08T14:37:02

The answer is #=-33/65#

We need

#cos^2x+sin^2x=1#

#cos(a+b)=cosacosb-sinasinb#

Here,

#u# and #v# are in quadrant #I#

#sin(u)=4/5#, #=>#, #cosu=sqrt(1-sin^2u)=sqrt(1-16/25)=3/5#

#cos(v)=5/13#, #=>#, #sinv=sqrt(1-cos^2v)=sqrt(1-25/169)=12/13#

Therefore,

#cos(u+v)=cosucosv-sinusinv#

#=3/5*5/13-4/5*12/13#

#=15/65-48/65=-33/65#