1. Solution

2. 1
2 2
cos2x + tan2x
1 ­ sin x + (sin x) =
cos2x
We know that the
1
2
cos x + (sin x)
2
identity 1 ­ sin2x
2
cos x 2
is equal to cos x

3. 1 2 2
2 2
cos x + tan x
1 ­ sin x + (sin x) =
2
cos x
We know that 2
the identity sin x
2
sin x
cos2x + cos2x
cos2x 2
is equal to tan x
2 2
cos x + tan x Q.E.D.