Question

How to prove (1-secx)/(1-cosx)=-secx

Answer 1

?

Answer 2

Keep in mind:

\( \sec \theta = \dfrac{1}{\cos \theta} \)

Answer 3

I know that, but How would I do the left side.

Answer 4

@Mertsj
(1-secx)\( \color{red}{/} \)(1-cosx)=-secx

Answer 5

Yes.

Answer 6

-secx becomes -1/cosx

Answer 7

\( \dfrac{1 - \sec x}{1 - \cos x} = - \sec x\)

\( \dfrac{1 - \dfrac{1}{\cos x}}{1 - \cos x} = - \sec x\)

\( \dfrac{ \dfrac{\cos x}{\cos x} - \dfrac{1}{\cos x}}{1 - \cos x} = - \sec x\)

\( \dfrac{ \dfrac{\cos x - 1}{\cos x} } {1 - \cos x} = - \sec x\)

\( \dfrac{ \dfrac{-(1 - \cos x)}{\cos x} } {1 - \cos x} = - \sec x\)

Answer 8

Sorry. I didn't see that division sign.

Answer 9

\(\dfrac{ {-(1 - \cos x)} } {(1 - \cos x) \cos x} = - \sec x \)

\(\dfrac{ -1 } {\cos x} = - \sec x \)

Answer 10

In step 2, how did you multiply cosx/cosx?

Answer 11

Wait, never mind

Answer 12

so its false?

Answer 13

Since 1/cos x = sec x, it is true.