Question

if 2 sin theta - 1 = 0 find the value of sec theta + tan theta = root 3
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Answer 1

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Answer 2

AnswEr :

$\Rightarrow2 \: \sin( \theta) - 1 = 0$

$\Rightarrow2 \: \sin( \theta) = 1$

$\Rightarrow\: \sin( \theta) = \dfrac{1}{2}$

• sin( 30° ) = $\frac{1}{2}$

$\Rightarrow \sin( \theta) = \sin(30 \degree)$

჻ The Value of θ = 30°

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• Now Let's Head to the Question ;

$\large\longrightarrow \sec( \theta) + \tan( \theta) = \sqrt{3}$

• putting the Value of ( θ )

$\large\longrightarrow \sec(30 \degree) + \tan(30 \degree) = \sqrt{3}$

• sec( 30° ) = $\frac{2}{ \sqrt{3} }$
• tan( 30° ) = $\frac{1}{ \sqrt{3} }$

$\large\longrightarrow \dfrac{2}{ \sqrt{3} } + \dfrac{1}{ \sqrt{3} } = \sqrt{3}$

$\large\longrightarrow \dfrac{(2 + 1)}{ \sqrt{3} } = \sqrt{3}$

$\large\longrightarrow \dfrac{3}{ \sqrt{3} } = \sqrt{3}$

• rationalizing the term

$\large\longrightarrow \dfrac{3}{ \sqrt{3} } \times \dfrac{ \sqrt{3} }{ \sqrt{3} } = \sqrt{3}$

$\large\longrightarrow \dfrac{3 \sqrt{3} }{ (\sqrt{3})^{2} } = \sqrt{3}$

$\large\longrightarrow \dfrac{ \cancel3 \sqrt{3} }{ \cancel3} = \sqrt{3}$

$\large\longrightarrow \sqrt{3} = \sqrt{3} \: \: \: \: \: \text{LHS = RHS}$