Which one applies?

Question

Which of the following is equivalent to cscαsin(α−β)  for all values of α and β for which cscαsin(α−β) is defined?



sinαcotβ−cosα

cosβ+tanαsinβ

cosαcotβ−sinα

cosβ−tanαsinβ

cosβ−cotαsinβ

Answer 1

Hi,

The correct answer is cosβ−cotαsinβ

because

cscαsin(α−β) = csca sin(a-b) = 1/sina [ sina cosb - cosa sinb ]

distribute: 1/sina * sina cosb - 1/sina *cosa sinb

after simplify : cosb - cosa/sina * sinb = cosb - cota * sinb

I hope it is useful,

Minoo