Question

1 + cos2a= (2)/(1 + tan^2a)

Answer 1

I guess that you have to prove this identity.
first notice that: \(\huge1+\tan^2a=\frac{cos^2a}{cos^2a}+\frac{sin^2a}{cos^2a}=\frac{1}{cos^2a}\)
so:
\(\huge1+cos2a=2cos^2a\)
then use formula: \(cos(2a)=cos^2a-sin^2a\)
so your equatio becomes:
\(\huge1+cos^2a-sin^2a=2cos^2a\)
as you should know: \(sin^2a+cos^2a=1\)
putting this in the last expretion gives the identity

Answer 2

Which double-angle or Half-angle identity would be used?

Answer 3

doublé angle

Answer 4

so the one above?