Question 929139
You typed:


Explain why there is no angle theta that satisfies cos =1/2 and sec=2 ?


However cosine, secant, and all other trig functions require an argument such as theta or 2*theta. Therefore we cannot answer your question completely; please re-post. If you meant cos theta = 1/2 and sec theta = 2, there is a value of theta, e.g. 60 degrees or pi/3 radians.