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If $x = Tan 15 °, y = Cosec 75 °$ and $Z = 4 Sin 18 °$ then

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z $<$ x $<$ y

x $<$ y $<$ z

y $<$ z $<$ x

x $<$ z $<$ y

answer is D.

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Detailed Solution

$x = t a n 15$

$x = 2 - \sqrt{3} = 2 - 1.73$

= 0.27

$y = cosec 75$

$= \frac{2 \sqrt{2}}{\sqrt{3} + 1} = 2 \sqrt{2} \frac{(\sqrt{3} - 1)}{2}$

$= \sqrt{6} - \sqrt{2}$

$= 2.44 - 1.41$

$= 1.03$

$z = 4 \cdot \sin 18$

$= 4 \cdot \frac{\sqrt{5} - 1}{4} = 2.23 - 1$

$= 1.23$

$x < y < z$

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