Question

how to verify frac(sec theta/ csc theta- cot theta -frac(sectheta/csc theta +cot theta = 2csc theta

Answer 1

\[\large\rm \frac{ \sec \theta }{ \csc \theta -\cot \theta } -\frac{ \sec \theta }{ \csc \theta +\cot \theta }=2\csc \theta \] like this ?

Answer 2

Yes

Answer 3

Can you please help

Answer 4

ye gimme a sec
let me do it
i'll try to find easy way

Answer 5

thanks

Answer 6

okay alright
so first we should write sec and csc in terms of sin or cos
csc = ??
sec equal what ? do you know ?

Answer 7

1/sin - csc and sec =1/cos

Answer 8

i meant csc=1/sin

Answer 9

yes right
first deal with the denominator\[\large\rm \frac{ \sec \theta }{ \color{ReD}{\csc \theta -\cot \theta }} -\frac{ \sec \theta }{\color{reD}{ \csc \theta +\cot \theta }}=2\csc \theta \] \[\huge\rm \frac{ \sec \theta }{ \frac{ 1 }{ \sin }-\frac{ \cos }{ \sin}} - \frac{ \sec \theta }{ \frac{ 1 }{ \csc }+\frac{ \cos }{ \sin } }\]
cot =cos over sin

Answer 10

Yes i got that far then i get stuck

Answer 11

\[\huge\rm \frac{ \sec \theta }{ \color{red}{\frac{ 1 }{ \sin }-\frac{ \cos }{ \sin}}} - \frac{ \sec \theta }{\color{red}{ \frac{ 1 }{ \csc }+\frac{ \cos }{ \sin } }}\]

find common denominator of red part

Answer 12

but i get 1/sin +cos/sin

Answer 13

1-cos/sin - 1+cos/sin

Answer 14

if you have some work show it to me
so i can find ur mistakes instead stating ovr

Answer 15

1-cos/ sin -1+cos/sin
sin/sin-sin/sin which equals 1 then i flip it to multiuply with 1/cos-1/cos

Answer 16

ugh gawd

Answer 17

brb
i should refresh the page its lagging

Answer 18

here is where i get lost

Answer 19

\[\large\rm \frac{ \sec }{ \frac{ 1+\cos }{ \sin } }-\frac{ \sec }{ \frac{ 1+\cos }{ \sin } }\]now multiply top with the reciprocal of the bottom fraction (change division to multiplication )
like for first one
\[\large\rm \sec \times \frac{ \sin }{ 1-\cos } - \sec \times \frac{ \sin }{ 1+\cos }\]

Answer 20

so then I get 1-cos(sec) /sin - 1+cos(sec)/sin

Answer 21

yes right we can change sec to 1 over cos \[\frac{ 1 }{ \cos } \times \frac{ \sin }{ 1-\cos } - \frac{ 1 }{ \cos } \times \frac{\sin }{ 1+\cos }\]
\[\frac{ \sin }{ \cos(1-\cos) } -\frac{ \sin }{ \cos (1+\cos) }\]
now find the common denominator

Answer 22

cos (1-cos)(1+cos)

Answer 23

yes right \[\huge\rm \frac{ \sin\color{reD}{(1+\cos )}-\sin\color{reD}{(1-\cos)} }{ \cos (1-\cos)(1+\cos) }\]
multiply sin with the denominator of 2nd fraction
and multiply numerator of 2nd fraction with the denominator of 1st fraction
that's how i got the red part
now distribute parentheses by sin at the top
and foil(1-cos)(1+cos)

Answer 24

sin+sin cos - sin-sin cos

Answer 25

then distribute?
sorry wrong

Answer 26

sign mistake
-sin times -cos = ?

Answer 27

yes foil (1-cos)(1+cos) which is at the denominator

Answer 28

sin+sin cos

Answer 29

cos (cos^2)

Answer 30

yes right \[\huge\rm \frac{ \sin +sincos-\sin +sincos }{ \cos(1-\cos)(1+\cos) }\]
now (1-cos)(1+cos ) = ?

Answer 31

now it's not just cos ^2
what do you get when you multiply first term by 1st term of 2nd parentheses