What we don't learn in the new curriculum standard is actually very simple reasoning

sinX=2sinX/2*cosX/2

Divide the whole right by a (sinx/2) 2+(cosx/2) 2.

Sinx = 2 tanx/2/1+(tanx/2) 2 can be obtained.

cosx= 1-(tanx/2)^2/ 1+(tanx/2)^2

tanx = 2 tanx/2/ 1-(tanx/2)^2

The principle is actually the same.

I hope to adopt a very tired one.