Question

How to write in terms of sinx and/or cosx and simplify for :
1. (secx-cosx)/(secx+cosx)
2.(secx-1)/(xsecx)
3.(1-tanx)/(sinx-cosx)

Answer 1

sec x is given as
\[\sec x =\frac{1}{\cos x}\]
tan x is given as
\[\tan x = \frac{\sin x}{\cos x}\]
that would be 1st part...

Answer 2

okay

Answer 3

so when u simplify for 1st question,are u getting
\[1-\cos^2 x\]
in the numerator?

Answer 4

and
\[1+\cos^2 x\]
in the denominator??

Answer 5

yeah, then do I make the numerator sin^2X?

Answer 6

yes,correct,as cos^2x + sin^x =1

Answer 7

go for 2nd one and tell what u get?

Answer 8

I get (1-cosx)/(cosx^2), is that right?

Answer 9

nopes,
numerator is correct...
where did x go in the denominator??
u should get:
\[\frac{1-\cos x}{x}\]
as final answer

Answer 10

oh, right... I multiplied them wrong at the denominator

Answer 11

and 3rd one?

Answer 12

Do I make tanx into sinx/cosx for the numerator first?

Answer 13

yes,do that

Answer 14

then multiply top and bottom by cosx?

Answer 15

yup,correct,go on....is something getting cancelled from numerator and denominator??
remember,u can write (cos x -sin x) as -(sin x -cos x)

Answer 16

oh, I see. So the final will be -(1/cosx)?

Answer 17

yes:) thats correct....its in terms of cos x
if answer is allowed in sec x then it would be -sec x

Answer 18

oh, thank you very much for helping!:) I appreciate it!

Answer 19

your welcome :)