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Can anyone help me solve the following trig equations.

$$\frac{\sec{A}+\csc{A}}{\tan{A} + \cot{A}} = \sin{A} + \cos{A}$$

My work thus far

$$\frac{\frac{1}{\cos{A}}+\frac{1}{\sin{A}}}{\frac{\sin{A}}{\cos{A}}+\frac{\cos{A}}{\sin{A}}}$$

$$\frac{\frac{\sin{A} + \cos{A}}{\sin{A} * \cos{A}}}{\frac{\sin{A}}{\cos{A}}+\frac{\cos{A}}{\sin{A}}}$$

But how would I continue?

My second question is

$$\cot{A} + \frac{\sin{A}}{1 + \cos{A}} = \csc{A}$$

My work is

$$\frac{\cos{A}}{\sin{A}} + \frac{\sin{A}}{1 + \cos{A}} = \csc{A}$$

I think I know how to solve this one by using a common denominator but I am not sure.

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    Once you obtain ${\sin A+\cos A\over\sin A\cos A}\over{\sin A\over\cos A}+{\cos A\over\sin A}$, multiply top and bottom by $\sin A\cos A$ (or, otherwise, simplify the fraction by first doing the addition downstairs).2012-07-16

3 Answers 3