Question

If 2 cos 2A= root 3 and A is acute
1. Sin square ( 75 - A ) + cos square ( 45 +A )

Answer 1

2 cos 2A= root 3
or , cos2A= (root3)/2
or, cos2A=cos30
or, 2A= 30
or, A=30/ 2
or, A=15 degree

Now,
Sin square ( 75 - A ) + cos square ( 45 +A )
=sin square (75-15) + cos square (45 + 15)
= sin square (60) + cos square (60)
= {root3/2}^2 +{1/2}^2
=(3/4) + (1/4)
=(3+1)/4
=4/4
=1