How do you verify the identity #cot(pi/2-x)=tanx#?

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Answer 1 · 2017-02-06T18:38:42

see below

Left Hand Side:

#cot(pi/2 -x)=cos(pi/2 -x)/sin(pi/2 -x)#

Use the formulas #cos(A-B)=cosAcosB+sinAsinB# and
#sin(A-B)=sinAcosB-cosAsinB#

#=(cos (pi/2)cosx+sin(pi/2)sinx)/(sin(pi/2)cosx-cos(pi/2)sinx#

#=(0*cosx+1*sinx)/(1*cosx-0*sinx)#

#=sinx/cosx#

#=tanx#

#:. = # Right Hand Side