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anonymous
 one year ago
Verify the identity.
cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x equals two times secant of x.
anonymous
 one year ago
Verify the identity. cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x equals two times secant of x.

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misty1212
 one year ago
Best ResponseYou've already chosen the best response.1lets see if we can write this in math ok?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{\cos(x)}{1+\sin(x)} +\frac{1+\sin(x)}{\cos(x)}\] right ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ cosx }{ 1+sinx }+\frac{ 1+sinx }{ cosx }= 2\sec x\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1yeah must be , since the answer is \(2\sec(x)\) lets do the addition and see it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because everything else cancels out. yay

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1lets do the addition and see it trick i learned via @satellite73 put \(\cos(x)=a\), and \(\sin(x)=b\) get \[\frac{a}{1+b}+\frac{1+b}{a}\] when you add you get \[\frac{a^2+(1+b)^2}{(1+b)a}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1nothing cancels yet, we gotta multiply out up top \[\frac{a^2+1+2b+b^2}{(1+b)a}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1then since \(a^2+b^2=1\) you have \[\frac{2+2b}{(a+b)a}=\frac{2(1+b)}{(1+b)a}=\frac{2}{a}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1replacing \(a\) by \(\cos(x)\) you are left with \[\frac{2}{\cos(x)}=2\sec(x)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1hope all steps are clear, it is easier to write with a and b instead of cosine and sine

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you!! @misty1212

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@misty1212 when you are done can you help me??

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1\[\color\magenta\heartsuit\]
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