Question

solve cos 40°+cos 80°+cos 160°​

Answer 1

Answer:

0

Step-by-step explanation:

Formula to be applied : cosA+cosB= 2cos(A+B/2).cos(A-B/2)

cos40+cos80+cos120= 2cos(80+40/2).cos(80-40/2) + cos(160)

                              =2cos(180/2).cos(40/2) + cos(160)

                              =2cos(60).cos(20) +cos(160)

                              = 2(1/2). cos(20) + cos(160)    [Since cos(60)=1/2]

                               =cos(20) + cos(160)

                               =2cos(160+20/2).cos(160-20/2)

                               =2cos(90).cos(70)                 [Since cos(90)=0]

                               =0

hope it helps!!!!

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Answer 2

cos 40=cos (60-20)=cos 60 cos 20+sin 60 sin20

cos 80= cos (60+20)=cos 60 cos 20- sin 60 sin 20

cos 160=cos (180-160)= -cos 20

cos 240=cos (180+60)=-cos 60=-1/2

in second quant sin is positive

3rd quant tan is positive

sub all

cos 60 cos 20 + sin 60 sin 20+ cos 60 cos 20 - sin 60 sin 20-cos 20-1/2

= 2cos 60 cos 20- cos 20 -1/2

=cos 20(2(1/2)-1)-1/2

cos 20(0)-1/2

ans=-1/2