Question

I’m not sure what i’m supposed to do here please help me! I appreciate it!

Answer 1

1. 1/C^2

2. C^2

Answer 2

Problem 1

`1+\tan^2(\text{x}) = 1+\left(\frac{\sin(\text{x})}{\cos(\text{x})}\right)^2\\\\1+\tan^2(\text{x}) = 1+\frac{\sin^2(\text{x})}{\cos^2(\text{x})}\\\\1+\tan^2(\text{x}) = \frac{\cos^2(\text{x})}{\cos^2(\text{x})}+\frac{\sin^2(\text{x})}{\cos^2(\text{x})}\\\\1+\tan^2(\text{x}) = \frac{\cos^2(\text{x})+\sin^2(\text{x})}{\cos^2(\text{x})}\\\\1+\tan^2(\text{x}) = \frac{1}{\cos^2(\text{x})}\\\\1+\tan^2(\text{x}) = (1)/(C^2)\\\\`

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Answer:
`\displaystyle (1)/(C^2)`

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Problem 2

`(1-\sin(\text{x}))(1+\sin(\text{x})) = 1 - \sin^2(\text{x})\\\\(1-\sin(\text{x}))(1+\sin(\text{x})) = \cos^2(\text{x})\\\\(1-\sin(\text{x}))(1+\sin(\text{x})) = C^2\\\\`

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Answer:
`\displaystyle C^2`