- #1

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sqrt of ((1-sinx)/(1+sinx))= |secx-tanx|

i tried:

=|secx-tanx|

=|(1/cosx)-(sinx/cosx)|

=|(1-sinx)/cosx|

and i need it to equal the other side without touching the other side... please HELP!!!

- Thread starter Gill
- Start date

- #1

- 6

- 0

sqrt of ((1-sinx)/(1+sinx))= |secx-tanx|

i tried:

=|secx-tanx|

=|(1/cosx)-(sinx/cosx)|

=|(1-sinx)/cosx|

and i need it to equal the other side without touching the other side... please HELP!!!

- #2

AKG

Science Advisor

Homework Helper

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Hint: [itex]|A| = \sqrt{A^2}[/itex]

Hint: [itex]\cos ^2x + \sin ^2x = 1[/itex]

Hint: [itex]\cos ^2x + \sin ^2x = 1[/itex]

- #3

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sorry but that still seems to not work, wat can i do? am i doing something wrong?

- #4

lurflurf

Homework Helper

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on the sqrt side you could multiply the numerator and denominator by 1-sin(x)Gill said:

sqrt of ((1-sinx)/(1+sinx))= |secx-tanx|

i tried:

=|secx-tanx|

=|(1/cosx)-(sinx/cosx)|

=|(1-sinx)/cosx|

and i need it to equal the other side without touching the other side... please HELP!!!

and use (sin(x))^2=1-(cos(x))^2

on the other side write it in terms of sin and cos as you have but then writ cos in terms of sin (hit use sqrt).

- #5

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it works! thanks

- #6

AKG

Science Advisor

Homework Helper

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You must have been doing something wrong, because it does indeed work:Gill said:sorry but that still seems to not work, wat can i do? am i doing something wrong?

[tex]\left |\frac{1-\sin x}{\cos x}\right | = \sqrt{\frac{(1-\sin x)^2}{\cos ^2 x}} = \sqrt{\frac{(1-\sin x)^2}{1 - \sin ^2 x}} = \sqrt{\frac{(1-\sin x)^2}{(1 - \sin x)(1 + \sin x)}} = \sqrt{\frac{1-\sin x}{1 + \sin x}}[/tex]

Note that I cancelled a factor of [itex](1 - \sin x)[/itex] without checking that it wasn't 0. But you can check for yourself that if it is zero, then sin(x) = 1, which implies that cos(x) = 0, and so sec(x) and tan(x) are undefined, and I would assume that you're only asked to show that this identity holds for those values of x that don't lead to us having anything undefined (this happens when sec(x) or tan(x) are undefined, or when (1 + sin(x)) = 0).

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