SOLUTION: (sec x/ sin x) - (cos x/ sin x)

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Question 1012067: (sec x/ sin x) - (cos x/ sin x)
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
+%28sec+%28x%29%2F+sin+%28x%29%29+-+%28cos%28+x%29%2F+sin+%28x%29%29+ ............since sec+%28x%29+=1%2Fcos%28x%29, we have

= %28%281%2Fcos%28x%29%29%2F+sin+%28x%29%29+-+%28cos%28+x%29%2F+sin+%28x%29%29

= %281%2F%28cos%28x%29sin+%28x%29%29%29+-+%28cos%28+x%29%2F+sin+%28x%29%29.....common denominator is +cos%28x%29cos%28+x%29

= %281+-+cos%28x%29cos%28+x%29%29%2F+%28cos%28x%29sin+%28x%29%29

=%281+-+cos%5E2%28+x%29%29%2F+%28cos%28x%29sin+%28x%29%29............ since 1+-+cos%5E2%28+x%29=sin%5E2+%28x%29, we have

=sin%5E2%28x%29%2F+%28cos%28x%29sin+%28x%29%29

=sin%5Ecross%282%29+%28x%29%2F+%28cos%28x%29cross%28sin+%28x%29%29%29

=sin+%28x%29%2F+cos%28x%29

=tan%28x%29