- #1

paulmdrdo1

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Hey guys, I'm about to finish answering the chapter problems on my trigonometry books about proving Identities, there are 2 problems that made me scratch my head though. They are the last 2 problems left that I'm not yet able to verify. I would greatly appreciate it if you could lend me some hints to do these problems.

$\frac{1}{\left(\cos^{2}(x)-\sin^{2}(x)\right)^2}-\frac{4\tan^{2}(x)}{\left(1-\tan^{2}(x)\right)^2}=1$

$\frac{\tan(\theta)+\sec(\theta)-1}{\tan(\theta)-1\sec(\theta)+1}=\frac{1+\sin(\theta)}{\cos(\theta)}$

from here I have no idea what to do next. please help. Thanks!My attempt for prob1

$\frac{1}{\left(\cos^{2}(x)-\sin^{2}(x)\right)^2}-\frac{(4)\frac{\sin^{2}(x)}{\cos^{2}(x)}}{\left(1-\frac{\sin^{2}(x)}{\cos^{2}(x)}\right)^2}=1$$\frac{1-4\cos^{2}(x)\sin^{2}(x)}{\left(\cos^{2}(x)-\sin^{2}(x)\right)^2}=1$

$\frac{1}{\left(\cos^{2}(x)-\sin^{2}(x)\right)^2}-\frac{4\tan^{2}(x)}{\left(1-\tan^{2}(x)\right)^2}=1$

$\frac{\tan(\theta)+\sec(\theta)-1}{\tan(\theta)-1\sec(\theta)+1}=\frac{1+\sin(\theta)}{\cos(\theta)}$

from here I have no idea what to do next. please help. Thanks!My attempt for prob1

$\frac{1}{\left(\cos^{2}(x)-\sin^{2}(x)\right)^2}-\frac{(4)\frac{\sin^{2}(x)}{\cos^{2}(x)}}{\left(1-\frac{\sin^{2}(x)}{\cos^{2}(x)}\right)^2}=1$$\frac{1-4\cos^{2}(x)\sin^{2}(x)}{\left(\cos^{2}(x)-\sin^{2}(x)\right)^2}=1$

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