How does one prove the following equation? (Image attached for reference)
1 Answer
Apr 8, 2018
See below
Explanation:
Since I'm given 4 blanks, here's my approach:
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#sin(theta/2)/cos(theta/2)= sintheta/(1+costheta)#
Reason: Quotient Identity :#sintheta/costheta= tantheta# -
#(sqrt((1-costheta)/2))/(sqrt((1+costheta)/2))= sintheta/(1+costheta)#
Reason: Half angle Identities :#sin(theta/2)=sqrt((1-costheta)/2)# and#cos(theta/2)=sqrt((1+costheta)/2)# -
#(sqrt((1-costheta)/cancel2))*(sqrt(cancel2/(1+costheta)))= sqrt((1-costheta)/(1+costheta))=sintheta/(1+costheta)#
Reason: Division of fractions
#sqrt((1-costheta)/(1+costheta)*(1+costheta)/(1+costheta))= sqrt((1-cos^2theta)/(1+costheta)^2)=sqrt((sin^2theta)/(1+costheta)^2)= sintheta/(1+costheta) #
Reason: Rationalization of the denominator and modified Pythagorean identity: