How can I simplify this expression? Sin(ß)Cos(-ß)Csc(ß)

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Answer 1 · 2018-03-25T04:49:14

It simplifies to #cosbeta#.

Use the reciprocal definition, then the cosine difference formula:

#color(white)=sinbetacos(-beta)cscbeta#

#=sinbetacos(-beta)*1/sinbeta#

#=color(red)cancelcolor(black)sinbeta cos(-beta)*color(red)cancelcolor(black)(1/sinbeta)#

#=cos(-beta)#

#=cos(0-beta)#

#=cos0cosbeta+sin0sinbeta#

#=1*cosbeta+0*sinbeta#

#=1*cosbeta#

#=cosbeta#

That's it. Hope this helped!