Given $\tan \theta \sec \theta = 1,$ find \[\frac{1 + \sin \theta}{1 - \sin \theta} - \frac{1 - \sin \theta}{1 + \sin \theta}.\]
\(\tan \theta \sec \theta = 1,find \frac{1 + \sin \theta}{1 - \sin \theta} - \frac{1 - \sin \theta}{1 + \sin \theta}. \)
[ 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
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(1 + sin A) (1 - sin A)
(sIn^2A + 2sin A + 1) - ( sin^2A - 2sin A + 1)
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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