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
$1+csc(A))(1-sin(A))$

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

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

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

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

$=cot(A)*cos(A)$

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