Question

prove trig identity:

sinx tanx = secx - cosx

Answer 1

first, change tan(x) as sin(x)/cos(x)
so, sin(x) tan(x)
= sin(x) * sin(x)/cos(x)
= sin^2(x)/cosx

then use the identity :
sin^2(x) = 1 - cos^2 (x)

therefore
sin^2 (x)/cos(x)
= (1 - cos^2(x))/cos(x)
= 1/cos(x) - cos^2(x)/cos(x)
= sec(x) - cos(x)

Answer 2

what did you do at the last 3 lines
= (1 - cos^2(x))/cos(x)
= 1/cos(x) - cos^2(x)/cos(x)
= sec(x) - cos(x)
can you explain those?

Answer 3

that's just splite it into 2 parts. if given (a-b)/c then it would be a/c - b/c

Answer 4

ah ok thanks!

Answer 5

welcome