Our teacher gave us this problem to work on this week, but I think either he or someone else copied it down wrong. I have tried everything I can think of; see if any of you can get it:
1-sin(t) / cos(t) = cos(t) / 1-sin(t)
The classic identity is: . . . . or one its variations.
. . The two binomials must have opposite signs.
I've created dozens of identities for my student's exams.
Start with . . .
. . 1-\sin x)" alt="\cos^2\!x\:=\:1-\sin^2\!x \quad \Rightarrow\quad (\cos x)(\cos x) \:=\1-\sin x)" />
. . 1-\cos x)" alt="\sin^2\!x\:=\:1-\cos^2\!x \quad\Rightarrow\quad (\sin x)(\sin x) \:=\1-\cos x)" />
. . . See?