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) andcos(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: