Sharon posted an Question
April 14, 2020 • 05:27 am 30 points
  • IIT JAM
  • Biotechnology (BT)

Ifa +b+c=3pi/2 then cos 2a + cos 2b + cos 2c is ?

IfA +B+C=3Pi/2 then cos 2A + cos 2B + Cos 2C is ? The answer is given in the booklet but i want a detail description step wise for better understanding

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    Narayan singh best-answer

    As A+B+C=3π/2, we have A+B=(3π/2−C) and cos(A+B)=cos(3π/2−C)=−sinC Hence cos2A+cos2B+cos2C =2cos(2A+2B/2)cos(2A−2B/2)+cos2C =2cos(A+B)cos(A−B)+cos2C =2cos(3π/2−C)cos(A−B)+1−2sin2C =−2sinCcos(A−B)+1−2sin2C =1−2sinC(cos(A−B)−sinC) =1−2sinC(cos(A−B)+cos(A+B)) =1−2sinC(2sinAsinB) =1−4sinAsinBsinC for more clearly see attached image

    cropped4701767360228111881.jpg
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