Trig Identity Help (1 Viewer)

nrlwinner · Aug 16, 2009

Hi. I need some assistance on the following equations

Simplify:

1. $(sec^2\Theta -1)tan(90 \degree -\Theta )$

2. $1-sin^2(180+\Theta )$

3. $\frac{x^2}{\sqrt{x^2-a^2}} \;\;\;when x=asec\Theta$

4. $\sqrt{a^2-x^2}\;\;\;\; when x=acos\Theta$

Peal Moon · Aug 16, 2009

1 $tan\theta$
2 $sin^2\theta$
3 $acot\theta$
4 $asin\theta$

sidereal · Aug 16, 2009

1.
$(\sec^2 \theta - 1).\tan(90-\theta) \\ = (\tan^2 \theta).\cot\theta \text{, since } 90-\theta \text{ swaps } \sin\theta \text{ and } \cos\theta \\ = \tan\theta$

2.
$1-\sin^2(180 + \theta) \\ = 1-(\sin(180+\theta))^2 \\ = 1 - (-\sin\theta)^2 \\ = 1 - \sin^2 \theta \\ = \cos^2 \theta$

3.
$\frac{x^2}{\sqrt{x^2-a^2}}, \text{ let } x = a\sec\theta \\ = \frac{a^2 \sec^2\theta}{\sqrt{a^2(\sec^2 - 1)}} \\ = a\sec^2\theta \times \left|\cot\theta\right| \\ \text{from here you could go a number of ways...} \\$

4.
$\sqrt{a^2 - x^2}, \text{ let } x = a\cos\theta \\ = \sqrt{a^2(1-\cos^2\theta)} \\ = a\sqrt{\sin^2\theta} \\ = a\sin\theta$

nrlwinner · Aug 16, 2009

For question 3, the answer says it's $a sec\Theta cosec\Theta$

but I get $asin^2\Theta$

sidereal · Aug 16, 2009

Trig Identity Help (1 Viewer)

nrlwinner

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Peal Moon

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sidereal

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nrlwinner

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sidereal

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