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  • If for real values of x, cos⁡θ=x+1/x then A. θ is an acute angle B. θ is right angle C. θ is an obtuse angle D. No value of θ is possible

If for real values of x, \cos \theta =x+\frac{1}{x} then
A. θ is an acute angle
B. θ is right angle
C. θ is an obtuse angle
D. No value of θ is possible

Answers (1)

The answer is the option (d).   

\\\\ \cos \theta =x+\frac{1}{x}=\frac{x^{2}+1}{x} \\\\ x^{2} - x\cos \theta +1=0 \\\\ \text{For real value of x, } \left( b \right) ^{2} - 4 \times a \times c \geq 0 \\\\


\\ \left( - \cos \theta \right) ^{2} - 4 \times 1 \times 1 \geq 0 \\\\ \cos ^{2} \theta \geq 4 \\\\ \cos \theta \geq \pm 2 \\\\

Hence, correct option is (d).  

Posted by

infoexpert21

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