Question

1-sin^2a/cos2a+sin^2a

Answer 1

=1-cos^2a.................

Answer 2

We can start by simplifying the denominator first:

cos(2a) + sin^2(a) = cos^2(a) + sin^2(a) + sin^2(a) + cos^2(a) = 2cos^2(a) + sin^2(a) = sin^2(a) + cos^2(a) + cos^2(a) = 1 + cos^2(a)

Substituting this back into the original expression:

(1 - sin^2(a))/(1 + cos^2(a)) = cos^2(a)/(1 + cos^2(a))

Now we have a simpler expression that can be further simplified by factoring out cos^2(a) from the denominator:

cos^2(a)/(1 + cos^2(a)) = cos^2(a) * 1/(1 + cos^2(a)) = cos^2(a) * (1 - cos^2(a) + cos^2(a))/(1 + cos^2(a))

= cos^2(a) - cos^4(a) + cos^2(a)^2/(1 + cos^2(a))

= cos^2(a) - cos^4(a) + cos^4(a)/(1 + cos^2(a))

= cos^2(a) - cos^4(a)/(1 + cos^2(a))

Therefore, the final simplified expression is:

cos^2(a) - cos^4(a)/(1 + cos^2(a))