Complete the identity?

Question

#sin^2(theta/2) = ?#

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Answer 1 · 2018-05-28T04:33:28

#sin^2(theta/2)#

#=1/2(2sin^2(theta/2))#

#=1/2(sin^2(theta/2)+1-cos^2(theta/2))#

#=1/2(1-(cos^2(theta/2)-sin^2(theta/2))#

#=1/2(1-(cos(theta/2)xxcos(theta/2)-sin(theta/2)xxsin(theta/2))#

#=1/2(1-costheta)#

Answer 2 · 2018-05-28T04:37:54

#color(maroon)(=>(1 - cos theta)/2#

#sin^2 (theta/2)#

#1 - 2 sin^2 x = cos (2x)#, identity

#=> (1 - cos (2 * (theta/2)))/2 = (1 - cos theta)/2#