Please help prove this trigonometric identity?!!! #(sinA-cosA)/(cosecA-sinA)=tan^2A-tanA#

#(sinA-cosA)/(cosecA-sinA)=tan^2A-tanA#

1 Answer
Jim G.
Feb 10, 2018

#"see explanation"#

Explanation:

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

#•color(white)(x)cscA=1/sinA" and "tanA=sinA/cosA#

#"consider the left side"#

#(sinA-cosA)/(1/sinA-sinA)#

#"multiply numerator/denominator by "sinA#

#=(sin^2A-sinAcosA)/(1-sin^2A)#

#=(sin^2A-sinAcosA)/cos^2A#

#=sin^2A/cos^2A-(sinAcancel(cosA))/(cancel(cosA)cosA)#

#=sin^2A/cos^2A-sinA/cosA#

#=tan^2A-tanA=" right side"#

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