question_answer

If\[\tan \theta +\sec \theta =2\], \[0\le \theta \le \frac{\pi }{2}\]find the value of the\[\tan \theta \].

A)  \[\frac{3}{4}\]                                                  

B)  \[\frac{5}{4}\]  

C)  \[\frac{3}{2}\]                                  

D)         \[\frac{5}{2}\]

Correct Answer: A

Solution :

 Solving the question from the options, we get \[\Rightarrow \]               \[p(-1)={{(-1)}^{2}}+3(-1)-2=(-4)\]           \[p(-1)=-4\] (Pythagoras theorem) \['x'\]\[1441\times x=5040\times 12\] Which satisfies the given equation.