SOLUTION (Question:253391.0)

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Sonu

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SOLUTION (Question:253391.0)

how did we come from 5th line to 6th

Question:

Minimum value of $1 + 2 t a n^{2} θ + 3 c o s^{2} θ$ is.

Options:

$3 + 2 \sqrt{6}$

$2 \sqrt{6} - 1$

$3 + \sqrt{6}$

Solution:

$1 + 2 t a n^{2} θ + 3 c o s^{2} θ$

$1 + 2 (s e c^{2} θ - 1) + 3 c o s^{2} θ$

$= 1 + 2 s e c^{2} θ - 2 + 3 c o s^{2} θ$

$= 2 s e c^{2} θ + 3 c o s^{2} θ - 1$

$= 3 c o s^{2} θ + 2 s e c^{2} θ - 1$

$= (\sqrt{3} c o s θ - \sqrt{2} s e c θ) + 2 \sqrt{6} - 1$

So minimum value is $(2 \sqrt{6} - 1)$

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SOLUTION (Question:253391.0)

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