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(1+cos alpha)(1+cos beta)(1+cos gamma ) =(1-cos alpha ) ( 1-cos beta ) ( 1-cos gamma ) Show that the valus of each member of the equation is ( sin alpha ) ( sin beta ) ( sin gamma )

(1+cos alpha)(1+cos beta)(1+cos gamma ) =(1-cos alpha ) ( 1-cos beta ) ( 1-cos gamma ) Show that the valus of each member of the equation is ( sin alpha ) ( sin beta ) ( sin gamma )

Grade:10

1 Answers

Priyansu Mishra
15 Points
5 years ago
(1 + Cos alpha )( 1 + cos beta )( 1 + cos gamma) / ( 1 – cos alpha )( 1 – cos beta )( 1 – cos gamma )  =1
 
multiplying (1+ cos alpha)( 1+ cos beta )( 1+ cos gamma ) in both numerator and denominator ,
 
[(1 + cos alpha )( 1+ cos beta )( 1+ cos gamma )]2  / (1 – cos2alpha )( 1 – cos2beta )( 1 – cos 2gamma )  = 1
 
[(1 + cos alpha )( 1+ cos beta )( 1+ cos gamma )]2  /  (sin2alpha)( sin2beta )( sin2gamma)   = 1
 
 
[(1 + cos alpha )( 1+ cos beta )( 1+ cos gamma )]2  =  (sin2alpha)( sin2beta )( sin2gamma)
 
 
(1 + cos alpha )( 1+ cos beta )( 1+ cos gamma )  = (sin alpha)( sin beta )( sin gamma)
 
 
hence , proved.....................................
 

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