Question #4ae15

1 Answer
Apr 24, 2016

Use the facts that:
XXXsin(x)cos(x)=tan(x)
and
XXX1sin2(x)=cos2(x)

Explanation:

Note that I have assumed that the intended requirement was to show that:
XXXcos(x)1sin(x)cos(x)1+sin(x)=2tan(x)
(as expressed in the question the expression is ambiguous)

cos(x)1sin(x)cos(x)1+sin(x)

XXX=(cos(x))(1+sin(x))(1sin(x))(1+sin(x))(cos(x))(1sin(x))(1+sin(x))(1sin(x))

XXX=(cos(x)+cos(x)sin(x))(cos(x)cos(x)sin(x))1sin2(x)

XXX=2cos(x)sin(x)cos2(x)

XXX=2sin(x)cos(x)

XXX=2tan(x)