How do you prove #(1 + csc A)(1 - sin A) = cotA cosA#?

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Answer 1 · 2015-05-02T22:11:52

Remember that
#csc(A) = 1/sin(a)#
and
#cot(A) = cos(A)/sin(A)#

Therefore
#1+csc(A))(1-sin(A))#

#=1+1/sin(A)-sin(A)-sin(A)/sin(A)#

#=(1-sin^2(A))/sin(A)#

#=cos^2(A)/sin(A)#

#= cos(A)/sin(A) * cos(A)#

#=cot(A)*cos(A)#