explain (Question:325751.0)

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TRINA DAS

· started a discussion

· 1 Months ago

explain (Question:325751.0)

How does the first line of the detailed solution come?

Question:

If $(r c o s θ - \sqrt{3})^{2} - (r s i n θ - 1)^{2} = 0$ then the value of $\frac{r t a n θ + s e c θ}{r s e c θ + t a n θ}$ is

Options:

$\frac{4}{5}$

$\frac{\sqrt{3}}{4}$

$\frac{\sqrt{5}}{4}$

$\frac{5}{4}$

Solution:

$\begin{matrix} r c o s θ = \sqrt{3} r s i n θ = 1 \\ c o s θ = \frac{\sqrt{3}}{r} . . . . (i) s i n θ = \frac{1}{r} . . . . (i i) \\ f r o m (i) (i i) \\ t a n θ = \frac{1}{\sqrt{3}} \Rightarrow θ = 3 0^{0} \\ f r o m e q . (i) r = 2 \\ s o r = 2 θ = 3 0^{0} \\ N o w, \frac{2 t a n 3 0^{0} + s e c 3 0^{0}}{2 s e c 3 0^{0} + t a n 3 0^{0}} \\ = \frac{\frac{2}{\sqrt{3}} + \frac{2}{\sqrt{3}}}{\frac{4}{\sqrt{3}} + \frac{1}{\sqrt{3}}} = \frac{4}{5} \end{matrix}$

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explain (Question:325751.0)

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