See the pic carefully and solve It is from chapter compound angles

I got the value as 2. First I get relation that a^2+b^2= c^2+d^2. By solving c-dtan20 = -bsec20 and d+ctan20 = -asec20. Then I also got by solving above two equtn. that b^2=c^2cos^2(20) - d^2sin^2(20) +2bdsin20 and a^2=d^2cos^2(20) - c^2sin^2(20) -2acsin20. By putting them in first relation I get (c^2+d^2)[cos^2(20) - sin^2(20)] +2( bd-ac)sin20 =c^2+d^2 .So by solving above you will get the required value that is 2.

Approved