How can this be reduced to the simplest form?

#(cos^2x)/(sinx) + sinx#

2 Answers
Mar 6, 2018

#cscx#

Explanation:

#"express as a single fraction"#

#=cos^2x/sinx+sin^2x/sinx#

#=(cos^2x+sin^2x)/sinxlarrcolor(blue)"single fraction"#

#=1/sinx#

#=cscx#

Mar 6, 2018

#color(blue)(csc theta#

Explanation:

#(cos2x) / sin x + sin x #

#=> (cos^2 x + sin ^2x) / sin x#. Taking LCM as sin x.

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But #cos^2 theta + sin ^2 theta = 1#

#=> 1 / sin theta = csc theta#