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Which one of the following equations has no real solutions? Tick (✓) one box - AQA - A-Level Maths Pure - Question 2 - 2020 - Paper 2
Question 2
Which one of the following equations has no real solutions? Tick (✓) one box. cot.x = 0 ln.x = 0 |x + 1| = 0 sec.x = 0 [1 mark]
Worked Solution & Example Answer:Which one of the following equations has no real solutions? Tick (✓) one box - AQA - A-Level Maths Pure - Question 2 - 2020 - Paper 2
Step 1
sec.x = 0
Answer
The function \( ext{sec}\) is defined as \( ext{sec}(x) = rac{1}{ ext{cos}(x)}\). This function is undefined when \( ext{cos}(x) = 0\), which occurs at odd multiples of \( rac{ ext{π}}{2}\). Therefore, there are no values of \( ext{x}\) for which \( ext{sec}(x) = 0\) has real solutions. Thus, the correct box to tick is for \( ext{sec}(x) = 0\).