cos^-1x-cos^-1y/2=a

xy/2+1-x^2.4-y^2/2=cosa

(cosa-xy/2)^2=(1-x^2.4-y^2/2)^2

solve u will get the exact eq with ans =4sin^2a

20 cos^2x=5+sinx+3cosx

20cos^2x-5=2cosx-/3

5(4cos^2x-1)=2cosx-3

5(2cos^x+cos2x)=2cosx-/3

LHS min=5

rhs max2

2cos^x+cos2x=o and cosx-/3=0

solve get ans

in triangle ABC Ra,Rb,Rc  R THE RADII OF THE CIRCLES WHICH TOUCHTHE INCIRCLE ND THE SIDES EMANTING FROM THE VERTICES A,B,C RESPECTIVELY .PROVE THAT

         (Ra.Rb)^1/2   +(Rb.Rc)^1/2   +(Rc.Ra)^1/2   =r

A1B1C1 R THE INTERIOR POINTS OF THE SIDES AC ,AB,BC RESPECTIVELY PROVE THAT:

 

         AREA A1B1C1/AREAOFABC   1/COSEC^2A+COSEC^2B+COSEC^2C