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

Question

1327 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-25T04:49:14

It simplifies to $cos β$ $cosbeta$ .

Use the reciprocal definition, then the cosine difference formula:

$= sin β cos (- β) csc β$ $color(white)=sinbetacos(-beta)cscbeta$

$= sin β cos (- β) \cdot \frac{1}{sin β}$ $=sinbetacos(-beta)*1/sinbeta$

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

$=cos(-beta)$

$=cos(0-beta)$

$=cos0cosbeta+sin0sinbeta$

$=1*cosbeta+0*sinbeta$

$=1*cosbeta$

$=cosbeta$

That's it. Hope this helped!