Let f(θ) is distance of line ( √ {sin θ } )x + ( √ {cos θ })y +1 = 0 from origin.

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1.Relation and Function

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Let $f(\theta)$ is distance of the line $( \sqrt {\sin \theta } )x + ( \sqrt {\cos \theta })y +1 = 0$ from origin. Then the range of $f(\theta)$ is -

A

$\left[ {\frac{1}{{{2^{\frac{1}{4}}}}},\infty } \right)$

B

$\left[ {1,\sqrt 2 } \right]$

C

$[{1},{\infty } )$

D

$\left[ {\frac{1}{{{2^{\frac{1}{4}}}}},1 } \right]$

Solution

$f(\theta)=\frac{1}{\sqrt{\sin \theta+\cos \theta}}$

$\theta \in\left[0, \frac{\pi}{2}\right]$

Maximum value $=\frac{1}{0+1}=1$

minimum value $ = \frac{1}{{\sqrt 2 }} = \frac{1}{{{2^{1/4}}}}$

Standard 12

Mathematics

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