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Precalculus Mathematics Homework Help
Proving trigonometric functions
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[QUOTE="Mentallic, post: 4895189, member: 144450"] You're welcome :) Also, notice something. We want to prove that [tex]\frac{1}{\sec\theta-\tan\theta}=\sec\theta+\tan\theta[/tex] So what if we simply multiplied the LHS by the conjugate of the denominator, resulting in [tex]\frac{1}{\sec\theta-\tan\theta}\cdot \frac{\sec\theta+\tan\theta}{\sec\theta+\tan\theta}[/tex] [tex]=\frac{\sec\theta+\tan\theta}{\sec^2\theta-\tan^2\theta}[/tex] and at this point we know that it's supposed to be equal to the RHS (since you're expecting the result to be true), so clearly the denominator must be equal to 1. Well can we show that? [tex]\sec^2\theta-\tan^2\theta=1[/tex] should remind you of the identity [tex]\sec^2\theta=1+\tan^2\theta[/tex] so if you mention this identity, then you can say that the denominator is equal to 1 and hence you've proved it without ever converting to sin and cos. [/QUOTE]
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Precalculus Mathematics Homework Help
Proving trigonometric functions
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