How to prove #cos^2(theta/2) = (1+sectheta)/(2sectheta)#? Thanks in advance

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Answer 1 · 2018-04-06T06:02:56

Please go through a Proof given in Explanation.

Recall that, #2cosalphacosbeta=cos(alpha+beta)+cos(alpha-beta)#.

Now, #cos^2(theta/2)=1/2{2cos(theta/2)cos(theta/2)}#,

#=1/2{cos(theta/2+theta/2)+cos(theta/2-theta/2)}#,

#=1/2(costheta+1)#,

#=1/2(1/sectheta+1)#,

#=(1+sectheta)/(2sectheta)#, as desired!

Answer 2 · 2018-04-06T09:03:37

Kindly refer to another Proof in the Explanation.

Using, #1+cos2x=2cos^2x#, we can prove this as shown below :

#(1+sectheta)/(2sectheta)=1/2{1/sectheta+sectheta/sectheta}#,

#=1/2{costheta+1}=1/2{2cos^2(theta/2)}=cos^2(theta/2)#.