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Given $\tan \theta \sec \theta = 1,$ find \[\frac{1 + \sin \theta}{1 - \sin \theta} - \frac{1 - \sin \theta}{1 + \sin \theta}.\]

 Oct 15, 2019
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\(\tan \theta \sec \theta = 1,find \frac{1 + \sin \theta}{1 - \sin \theta} - \frac{1 - \sin \theta}{1 + \sin \theta}. \)

 

 

[ I'm using  A  instead of  Theta ]

 

 

1 +  sin A           1  - sin A

_______    -    __________        get a common denominator

1  - sin A            1 +   sin A

 

(1 + sinA)^2  - (1 - sin A)^2

_______________________

(1 + sin A) (1 - sin A)

 

 

(sIn^2A  + 2sin A  + 1)   - ( sin^2A - 2sin A + 1)

_______________________________________

               1  -  sin^2 A

 

 

2 sin A  +  2 sin A

_______________

        cos^2 A

 

 

  4 sin A

_______

 cos^2 A

 

 

    4 sin A

____________

cos A * cos A

 

 

4 * sin A  *   1

    _____    ____

     cos A    cos A

 

4   ( tan A   sec A )

 

4     (1)   =

 

4

 

 

cool cool cool

 Oct 15, 2019

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