how can i prove that cos(x+y).cos(x-y)=cos^2(x)+cos^2(y)-1
Answers
Answered by
0
Step-by-step explanation:
xbsusisvvsbaoajabbsjsbsvshsu s syzgacacagava ysvs
Answered by
0
Answer:
Step-by-step explanation:
C=cos^2(x)+cos^2(y)-1
LHS = cos(x+y).cos(x-y)
=( cosxcosy-sinxsiny) ( cosxcosy + sinxsiny)
=cos²xcos²y - sin²x sin²y
=cos²xcos²y -(1-cos²x)-(1-cos²y)
=cos²xcos²y -( 1-cos²y-cos²x+cos²ycos²x)
=cos²xcos²y-1+cos²y+cos²x-cos²xcos²y
=cos²x+cos²y-1=RHS
=(1-sin²x)(cos²y) - ( 1-cos²x)(sin²y)
=cos²y-sin²xcos²y-sin²y+cos²xsin²y
=cos²y-sin²y-sin²xcos²y+cos²sin²y
=cos²y-sin²y-
Similar questions