How do you verify the identity: #cosx cscx/cot^2x=Tanx#?

2 Answers
G_Dub
Apr 7, 2018

#cosx(cscx)/(cot^2x)#

#=cosx(1/sinx)/(cos^2x/sin^2x)#

#=cosx(sin^2x)/(sinxcos^2x)#

#=sinx/cosx#

#=tanx#

Jim G.
Apr 7, 2018

#"see explanation"#

Explanation:

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

#•color(white)(x)cscx=1/sinx" and "cotx=cosx/sinx#

#•color(white)(x)cotx=1/tanxhArrtanx=1/cotx#

#"consider the left side"#

#cosx xx(1/sinx)/(cot^2x)#

#=(cosx/sinx)/cot^2x#

#=cotx/cot^2x#

#=1/cotx=tanx="right side "rArr"verified"#

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