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anonymous
 one year ago
how do i verify
(cos x/ 1 + sin x) + (1 + sin x/ cos x) = 2 sec x?
i don't know how to verify anything at all can someone explain how it works?
anonymous
 one year ago
how do i verify (cos x/ 1 + sin x) + (1 + sin x/ cos x) = 2 sec x? i don't know how to verify anything at all can someone explain how it works?

This Question is Closed

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[\huge\rm \frac{ \cos(x) }{ 1+\sin(x) } +\frac{ 1+\sin(x) }{ \cos(x) }\] 1)what is the common denominator ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i really dont know anything about this

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3alright let's change that to `simple` algebra

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[\huge\rm \frac{ x }{ y }+\frac{ y }{ x }\] what's the common denominator ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3okay let's say y represent 1+sinx and x = cos(x) \[y=1+\sin(x)\] \[x=\cos(x)\] now can you tell me what would be the common denominator\[\huge\rm \frac{ \cos(x) }{ 1+\sin(x) } +\frac{ 1+\sin(x) }{ \cos(x) }\] for this question :=)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[\huge\rm \frac{ \cos(x) }{ \color{red}{1+\sin(x)} } +\frac{ 1+\sin(x) }{\color{blue}{ \cos(x)} }\] \[\huge\rm \frac{ \cos(\color{blue}{cos}) + (\color{reD}{1+\sin})(1+\sin)}{ \cos(x) (1+\sin(x))}\] multiply the numerator of `1st fraction` by the `denominator` of 2nd fraction multiply the numerator of `2nd fraction` with the denominator of `1st fraction`

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would it become cos^2x and (1+sin)^2 on the numerator??

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[(1+\sin(x))^2 = (1+\sin)(1+\sin)\] (1+sin)^2 is same as (1+sin)(1+sin) foil it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and what happens when i foil it?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3you will get 3 terms :3

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3then you will be able to cancel out some stuff at the numerator :=)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 1+2sinx+sin^2x ???

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3yes right \[\huge\rm \frac{ \color{ReD}{cos^2x}+1+2sinx+\sin^2x }{ cosx(1+sinx) }\] cos^2x= what ? familiar with the identity ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[\huge\rm sin^2 \theta+\cos^2\theta=1\] this one solve for cos^2

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3replace cos^2 with 1sin^2 and then simplify !

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[\huge\rm \frac{ \color{ReD}{1sin^2x}+1+2sinx+\sin^2x }{ cosx(1+sinx) }\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3yes! what is common factor ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[\huge\rm \frac{ 2+2sinx }{ \cos(x)(1+sinx) }\] 2+sinx what is common in both terms?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3no first term is 2 and 2nd one is 2sinx so sinx isn't common

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3yes right take out the 2 what will you get ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3when you take out 2 from 2 what will you have left wth?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3haha well no in other words you have to divide both terms with the common factor so \[\huge\rm \frac{ 2}{ 2} +\frac{ 2sinx }{ 2 } =2(??+???)\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3yes! and we should keep the common factor outside the parentheses \[\huge\rm \frac{ 2(1+sinx) }{ cosx(1+sinx) }\]

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3yes right and last step ?

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3thats fine! 2/cosx is same as \[\huge\rm 2 \times \frac{ 1 }{ cosx }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i honestly have no idea how to do anything with identities so thank you

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3ikr! trig is FUN(well i hate graph)

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3my pleasure! :=) welcome to openstudy!

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\(\color{blue}{\text{Originally Posted by}}\) @rami2021 salam alakom \(\color{blue}{\text{End of Quote}}\) Walikum salam and yeah arabic is my fvt language but all i know is *kafya halik ?? ;~;

Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3sorry about that alejand :3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i'm about to post another question, i have one left
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