Question

if a + b + c is equals to 270 then prove that sin a cos b sin c + cos a sin b sin c + sin a sin b cos c = cos a cos b cos c​

Answer 1

Answer:

$Solution,\\a +b+c=270\\or, a +b = 270-c$

$cos(a+b) = cos(270-c)~~~~~~~~~and~~~~~~~~~sin(a+b)=sin(270-c)\\or, cos(a+b) = -sinc,~sin(a+b) = -cosc\\Now,\\L.H.S. = sina.cosb.sinc +cosa.sinb.sinc + sina.sinb.cosc\\~~~~~~~~~~= sinc (sina.cosb+cosa.sinb)+sina.sinb.cosc\\~~~~~~~~~~=sinc[sin(a+b)]+sina.sinb.cosc\\~~~~~~~~~~=sinc.-cosc+sina.sinb.cosc\\~~~~~~~~~~=cosc(sina.sinb-sinc)\\~~~~~~~~~~=cosc[sina.sinb+cos(a+b)]\\~~~~~~~~~~=cosc[sina.sinb+cosa.cosb-sina.sinb]\\~~~~~~~~~~=cosc.cosa.cosb\\~~~~~~~~~~=cosa.cosb.cosc$

Hope I helped you!