Question
Question: The value of a for which the equation 4cosec<sup>2</sup>(π (a + x)) + a<sup>2</sup> – 4a = 0 has a ...
The value of a for which the equation
4cosec2(π (a + x)) + a2 – 4a = 0 has a real solution, is
A
a = 1
B
a = 2
C
a = 10
D
None of these
Answer
a = 2
Explanation
Solution
Here 4 [1 + cot2 π(a + x)] + a2 – 4a = 0
⇒ 4cot2π (a + x) + (a – 2)2 = 0
⇒ a – 2 = 0 and cot2π (a + x) = 0 ⇒ a = 2