How can this be reduced to the simplest form?

#(secx * sinx)/(tanx+cotx)#

1 Answer
Jim G.
Mar 6, 2018

#sin^2x#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)secx=1/cosx" and "cotx=1/tanx#

#•color(white)(x)tan^2x+1=sec^2x#

#rArr(1/cosx xxsinx)/(tanx+1/tanx)#

#=tanx/(tanx+1/tanx)xxtanx/tanx#

#=tan^2x/(tan^2x+1)#

#=tan^2x/sec^2x#

#=sin^2x/cancel(cos^2x) xxcancel(cos^2x)#

#=sin^2x#

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