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If for real values of x, cosA = x+1/x,then A) A is an acute angle B) A is a right angle C) A is an obtuse angle

If for real values of x, cosA = x+1/x,then
 
A) A is an acute angle
B) A is a right angle
C) A is an obtuse angle

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find the answer to your question below
cosA = x + \frac{1}{x}
-1\leq cosA\leq 1
-1\leq x + \frac{1}{x}\leq 1
-1\leq \frac{x^{2} + 1}{x}\leq 1
-x\leq x^{2} + 1\leq x
x^{2} + x + 1 \geq 0
It is possible, because
\Delta < 0
x^{2} - x + 1\leq 0
Not possible, because
\Delta < 0
So cosA will be negative which means A should be b/w (pi)/2 & pi.
(c) is a correct option.

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