Question

Verify the identity.

quantity one minus sine of x divided by cosine of x equals cosine of x divided by quantity one plus sine of x

Answer 1

looks like this
\[\frac{ 1 - sinx }{ cosx } = \frac{ cosx }{ 1 + sinx }\]

Answer 2

cross multiply ?

Answer 3

or i would solve right to make it equal

Answer 4

right side*

Answer 5

ok. so how would I start with right side?

Answer 6

you need to multiply denominator and numerator by the conjugate of 1+sinx

Answer 7

ahh ok

Answer 8

so it is
\[\frac{ cosx - sinxcosx }{ 1-\sin^2x}\]

Answer 9

okay so you don't need to distribute 1-sinx by cosx at the numerator \[\frac{ \cos(x)(1-\sin(x)) }{ 1-\sin^2 }\]
apply the identity 1-sin^2x equal to what ?

Answer 10

cos^2x

Answer 11

so it would be
\[\frac{ cosx(1-sinx) }{ \cos^2x }\]

Answer 12

yes right cos^2x can be written as cos x times cos x \[\huge\rm \frac{ \cos(x)(1-\sin(x)) }{ cos(x) \times cos(x) }\]

Answer 13

so factor out top and bottom leaves me with
\[\frac{ 1-sinx }{ cosx }\]

Answer 14

yep

Answer 15

and thats it

Answer 16

ty!

Answer 17

yep

Answer 18

my pleasure!