How do you prove #(1+sinx)/cosx = cotg( pi/4 - x/2)#? I need your help please !!!! :(

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Answer 1 · 2018-03-25T14:33:40

#LHS=(1+sinx)/cosx #

#=(cos^2(x/2)+sin^2(x/2)+2sin(x/2)cos(x/2))/(cos^2(x/2) -sin^2(x/2))#

#=(cos(x/2)+sin(x/2))^2/((cos(x/2) -sin(x/2))(cos(x/2)+sin(x/2))#

#=(cos(x/2)+sin(x/2))/(cos(x/2) -sin(x/2)#

#=(cos(x/2)/sin(x/2)+sin(x/2)/sin(x/2))/(cos(x/2)/sin(x/2) -sin(x/2)/sin(x/2))#

#=(cot(x/2)+1)/(cot(x/2) -1)#

#=(cot(x/2)cot(pi/4)+1)/(cot(x/2) -cot(pi/4))#

#= cot( pi/4 - x/2)=RHS#