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(sqrt(3)+2 sinA)^3/(1- 2cos A)^3+(1+ 2co...

`(sqrt(3)+2 sinA)^3/(1- 2cos A)^3+(1+ 2cos A)^3/(sqrt(3)-2 sinA)^3=`

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((sqrt(3)+2sin A)^(3))/((1-2cos A)^(3))+((1+2cos A)^(3))/((sqrt(3)-2sin A)^(3))=

((sqrt(3)+2sin A)^(3))/((1-2cos A)^(3))+((1+2cos A)^(3))/((sqrt(3)-2sin A)^(3))

The value of [(sqrt3 + 2sinP)/ (1- 2Cos P)]^3 + [(1 + 2Cos P )/(sqrt3-2sinP)]^3 is:

((sqrt(3)+2cos A)/(1-2sin A))^(-3)+((1+2sin A)/(sqrt(3)-2cos A))^(-3)=

((sqrt(3)+2cos A)/(1-2sin A))^(-3)+((1+2sin A)/(sqrt(3)-2cos A))^(-3)=

((sqrt(3) + 2 cosA)/( 1-2 sin A ))^(-3) + ((1+ 2 sin A )/( sqrt(3)-2 cos A ))^(-3) =

(sin3A)/(sinA)-(cos3A)/(cosA)=2

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then

(cos^3 A+sin^3 A) / (cos A+sinA) + (cos^3A-sin^3A) / (cos A-sin A) =2