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acos(cos^2+3sin^2)=pa
cos(cos^2+sin^2+ 2sin^2)=p
{As 3sin^2=sin^2 +2sin^2}
cos(1+2sin^2) =p. (1). {As. sin^2+cos^2=1}
similarly,
sin(1+2cos^2)= q. (2)
adding (1) and (2)
(cos(1+2sin^2) + sin(1+2cos^2))^2/3=(p+q)^2/3
similarly,
(cos(1+2sin^2)-sin(1+2cos^2))^2/3=(p-q)^2/3
(p+q)^2/3+(p-q)^2/3=2a^2/3
cos(cos^2+sin^2+ 2sin^2)=p
{As 3sin^2=sin^2 +2sin^2}
cos(1+2sin^2) =p. (1). {As. sin^2+cos^2=1}
similarly,
sin(1+2cos^2)= q. (2)
adding (1) and (2)
(cos(1+2sin^2) + sin(1+2cos^2))^2/3=(p+q)^2/3
similarly,
(cos(1+2sin^2)-sin(1+2cos^2))^2/3=(p-q)^2/3
(p+q)^2/3+(p-q)^2/3=2a^2/3
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