Question

Write each expression in terms of sine and​ cosine, and then simplify so that no quotients appear in the final expression and all functions are of theta only. (sec theta - csc theta )(cos theta + sin theta)

Answer 1

`\tan \theta-\cot \theta`

Explanation:

`(\sec \theta - \csc \theta)(\cos \theta + \sin \theta)= \\\\\\\left( (1)/(\cos \theta)-(1)/(\sin \theta) \right)(\cos \theta + \sin \theta)= \\\\\\\left( (1)/(\cos \theta) \cdot \cos \theta \right) + \left( (1)/(\cos \theta) \cdot \sin \theta \right) - \left( (1)/(\sin \theta) \cdot \cos \theta \right) - \left( (1)/(\sin \theta) \cdot \sin \theta \right)= \\\\\\1+(\sin \theta)/(\cos \theta)-(\cos \theta)/(\sin \theta) -1= \\\\\\\tan \theta-\cot \theta`

Hope this helps!