What is the simplified form of: (sinx + cosx)^2/(1+ 2*sin*x*cos x)

We'll recognize to denominator the double angle
identity:

2 sin x*cos x = sin
(2x)

We'll expand the binomial from
numerator:

(sin x)^2 + 2sin x*cos x + (cos
x)^2

We'll use the Pythagorean identity and we'll
get:

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

The numerator will become:

1
+ sin (2x)

Now, we'll re-write the
fraction:

(sinx + cosx)^2/(1+ 2*sin*x*cos x) = [1 + sin
(2x)]/[1 + sin (2x)]

(sinx + cosx)^2/(1+ 2*sin*x*cos x) =
1

The simplified fraction gives:(sinx +
cosx)^2/(1+ 2*sin*x*cos x) = 1