Question #1fa9c

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Answer 1 · 2017-10-15T08:09:44

# 7/25.#

#cosx+cosy=1/3 rArr 2cos((x+y)/2)cos((x-y)/2)=1/3.....(1).#

#sinx+siny=1/4 rArr 2sin((x+y)/2)cos((x-y)/2)=1/4.......(2).#

#:. (2) -: (1) rArr tan((x+y)/2)=3/4.#

Knowing that, #cos2theta=(1-tan^2theta)/(1+tan^2theta),# we have,

#cos(x+y)=cos(2((x+y)/2)),#

#=(1-tan^2((x+y)/2))/{1+tan^2((x+y)/2)},#

#=(1-9/16)/(1+9/16).#

# rArr cos(x+y)=7/25.#

Enjoy Maths.!