if 2 cos A/2=(root 1+sinA)+(root 1-sinA)then A/2 lies between?

Dear Student,
Please find below the solution to the asked query:

2cosA2=1+sinA+1-sinA2cosA2=cos2A2+sin2A2+2sinA2cosA2+cos2A2+sin2A2-2sinA2cosA22cosA2=cosA2+sinA22+cosA2-sinA222cosA2=cosA2+sinA2+cosA2-sinA2...iWe know thatx=xx0-xx0For i to be true, mod must open with positive sign i.e.cosA2+sinA20 and cosA2-sinA2012cosA2+12sinA20 and 12cosA2-12sinA20sinπ4cosA2+cosπ4sinA20 and sinπ4cosA2-cosπ4sinA20Multiply second inequality by -1sinπ4cosA2+cosπ4sinA20 and cosπ4sinA2-sinπ4cosA20sinA2+π40 and sinA2-π40sinA2+π40 and sin-A2+π40Now we make two graphs and see where they are positive together.

x0,π27π2,4πsinx2 has period of 4πx4,4+π24+7π2,4+4π

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