Identity Verification?

(cot^3(y)-tan^3(y))/(sec^2(y)+cot^2(y))=2cot(2y)

1 Answer
Feb 26, 2018

Verification of this identity in explanation page

Explanation:

#[(coty)^3-(tany)^3]/[(secy)^2+(coty)^2]#

=#[(coty)^3-(tany)^3]/[(tany)^2+1+(coty)^2]#

=#((coty-tany)*[(coty)^2+1+(tany)^2])/[(coty)^2+1+(tany)^2]#

=#coty-tany#

=#cosy/siny-siny/cosy#

=#[(cosy)^2-(siny)^2]/(siny*cosy)#

=#(cos2y)/(1/2sin2y)#

=#(2cos2y)/(sin2y)#

=#2cot2y#