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```
if A+B+C = pi/2, prove that cos^2A+cos^2B+cos^2C = 2+2 sinA sinB sinC

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2 years ago

```							=cos^2A+cos^2B+cos^2C=1-sin^2A+cos^2B+cos^2C=1+cos(A+B)cos(B-A)+cos^2C  ( cos^2B-sin^2A=cos(B+A)cos(B-A) )=1+sinCcos(B-A)+cos^2C=1+sinCcosAcosB +sinAsinBsinC+1-sin^2C=2+sinC(cosAcosB-sinC)+sinAsinBsinC=2+sinC(cosAcosB-cos(A+B))+sinAsinBsinC=2+sinC(sinAsinB)+sinAsinBsinC=2+2sinAsinBsinC.......Hope this helps..
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2 years ago
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