To simplify this expression, use the trigonometric identitycos^2(a) - sin^2(a) = cos(2a)
Therefore, the expression becomes(cos(2a) - 4sin^2(a)) / 2cos^2(a)
Next, factor out sin^2(a) from the numerator= (cos(2a) - 4sin^2(a)) / 2cos^2(a= cos(2a)/ 2cos^2(a) - 4sin^2(a) / 2cos^2(a= ((cos(2a)/ 2cos^2(a)) - 2sin^2(a) / cos^2(a)= (1/2 - 2tan^2(a))
Therefore, the simplified expression is: 1/2 - 2tan^2(a)
To simplify this expression, use the trigonometric identity
cos^2(a) - sin^2(a) = cos(2a)
Therefore, the expression becomes
(cos(2a) - 4sin^2(a)) / 2cos^2(a)
Next, factor out sin^2(a) from the numerator
= (cos(2a) - 4sin^2(a)) / 2cos^2(a
= cos(2a)/ 2cos^2(a) - 4sin^2(a) / 2cos^2(a
= ((cos(2a)/ 2cos^2(a)) - 2sin^2(a) / cos^2(a)
= (1/2 - 2tan^2(a))
Therefore, the simplified expression is: 1/2 - 2tan^2(a)