Question #9477a

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Answer 1 · 2017-11-30T07:28:05

The value is #=-1#

We need

#sin(a+b)=sinacosb+sinbcosa#

#cos(pi/4)=sin(pi/4)=1/sqrt2#

Therefore,

#cos(7pi)+sin(7pi)=sqrt2(1/sqrt2cos(7pi)+1/sqrt2sin(7pi))#

#=sqrt2(sin(pi/4)cos(7pi)+cos(pi/4)sin(7pi))#

#=sqrt2(sin(pi/4+7pi))#

#=sqrt2*(sin(pi/4+pi))#

#=sqrt2sin(-pi/4)#

#=sqrt2*-1/sqrt2#

#=-1#

Answer 2 · 2017-11-30T08:56:14

#cos7pi+sin7pi#

#=cos(4*2pi-pi)+sin(4*2pi-pi)#

#=cos(pi)-sin(pi)#

#=-1-0=-1#