Question

if sin ^2 theta -2 cos theta +1/4=0

Answer 1

sin²@-2cos@+1/4=0,

(1-cos²@)-2cos@+1/4=0,

1-cos²@-2cos@+1/4=0,

1+1/4=cos²@+2cos,
5/4=cos²@+2cos@,

5=4cos²@+8cos@,

then
4cos²@+8cos@-5=0,

4cos²@+(10-2)cos@-5=0,

4cos²@+10cos@-2cos@-5=0,

2cos@(2cos@+5)-1(2cos@+5)=0,

(2cos@+5)(2cos@-1)=0,

take
2cos@-1=0,

cos@=1/2,

cos@=cos60°,

then
@=60°