91Ó°ÊÓ

For the following exercises, simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. $$\sec x-\cos x$$

Simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. \(\quad(1+\tan \theta)^{2}-2 \tan \theta\)

For the following exercises, simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. $$(1+\tan \theta)^{2}-2 \tan \theta$$

Simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. \(\sin x(\csc x-\sin x)\)

For the following exercises, simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. $$\sin x(\csc x-\sin x)$$

Simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. \(\quad \frac{\cos t}{\sin t}+\frac{\sin t}{1+\cos t}\)

For the following exercises, simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. $$\frac{\cos t}{\sin t}+\frac{\sin t}{1+\cos t}$$

For the following exercises, simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. $$\frac{1+\tan ^{2} \alpha}{1+\cot ^{2} \alpha}$$

Simplify each expression by writing it in terms of sines and cosines, then simplify. The final answer does not have to be in terms of sine and cosine only. \(\frac{1+\tan ^{2} \alpha}{1+\cot ^{2} \alpha}\)

Verify that each equation is an identity. \(\frac{\tan \theta \cot \theta}{\csc \theta}=\sin \theta\)