Explain (Question:325745.0)

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TRINA DAS

· started a discussion

· 1 Months ago

Explain (Question:325745.0)

How does the last line come ? How does tanθ−cotθ =0 come?

Question:

The minimum value of $s i n^{2} θ + c o s^{2} θ + s e c^{2} θ + c o s e c^{2} θ + t a n^{2} θ + c o t^{2} θ$ is

Options:

Solution:

$\begin{matrix} (s i n^{2} θ + c o s^{2} θ) + (t a n^{2} θ + c o t^{2} θ) + (s e c^{2} θ + c o s e c^{2} θ) \\ = 1 + 1 + 1 + (t a n^{2} θ + c o t^{2} θ) 2 \\ = 3 + 2 (t a n^{2} θ + c o t^{2} θ) \\ = 3 + 2 (t a n^{2} θ + c o t^{2} θ) \\ = 3 + 2 (t a n^{2} θ + c o t^{2} θ - 2 + 2) \\ = 7 + (t a n θ - c o t θ)^{2} = 7 \end{matrix}$

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