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Trig Identity Homework due 5-7-14 (MRS22-3) or 5-8-14 (MRS22-1)

Prove each identity.

1. $\frac{\cot\theta}{\csc\theta}=\cos\theta$

2. $\cos^{2}x\tan^{2}x=\sin^{2}x$

3. $\frac{1-\sin^{2}\beta}{\cos\beta}=\cos\beta$

4. $\frac{\tan^{2}\alpha+1}{\sec\alpha}=\sec\alpha$

5. $1-\csc{x}\sin^{3}x=\cos^{2}x$

6. $\cos^{2}\theta(\tan^{2}\theta+1)=1$

7. $\sin^{2}\beta(1+\cot^{2}\beta)=1$

8. $\cot\theta+\tan\theta=\csc\theta\sec\theta$

9. $\sin^{2}\alpha+\tan^{2}\alpha+\cos^{2}\alpha=\sec^2\alpha$

10. $1+\csc^{2}x\cos^{2}x=\csc^{2}x$

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