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

Answer:

$\tan \theta-\cot \theta$

Step-by-step explanation:

$(\sec \theta - \csc \theta)(\cos \theta + \sin \theta)= \\\\\\\left( \dfrac{1}{\cos \theta}-\dfrac{1}{\sin \theta} \right)(\cos \theta + \sin \theta)= \\\\\\\left( \dfrac{1}{\cos \theta} \cdot \cos \theta \right) + \left( \dfrac{1}{\cos \theta} \cdot \sin \theta \right) - \left( \dfrac{1}{\sin \theta} \cdot \cos \theta \right) - \left( \dfrac{1}{\sin \theta} \cdot \sin \theta \right)= \\\\\\1+\dfrac{\sin \theta}{\cos \theta}-\dfrac{\cos \theta}{\sin \theta} -1= \\\\\\\tan \theta-\cot \theta$

Hope this helps!