Question

Solve this question​

Answer 1

Answer:

$\boxed{\huge{(3) \: \: \: 4\:\:\:}}$

Step-by-step explanation:

$\bold{To \: find}\longrightarrow \\ value \: of \: \\ \dfrac{1}{sin {10}^{0} } - \dfrac{ \sqrt{3} }{cos {10}^{0} }$

$\bold{Concept \: used}\longrightarrow \\ \boxed{sin( \alpha - \beta ) = sin \alpha \: cos \beta \: - cos \alpha \: sin \beta} \\\boxed{ 2 \: sin \alpha \: cos \alpha = sin2 \alpha}$

$\bold{Solution}\longrightarrow \\ \dfrac{1}{sin10 ^{0} } - \dfrac{ \sqrt{3} }{cos10 ^{0} }$

$= \dfrac{cos {10}^{0} - \sqrt{3} sin {10}^{0} }{sin {10}^{0} \: \: cos {10}^{0} }$

$dividing \: and \: multipying \: by \: 2 \: in \: numerator \\ = \dfrac{2 \: ( \dfrac{1}{2} cos {10}^{0} - \dfrac{ \sqrt{3} }{2} \: sin {10}^{0} )}{sin {10}^{0} \: \: cos {10}^{0} }$

$= \dfrac{2 \times 2(sin {30}^{0} \: cos {10}^{0} - cos {30}^{0} \: sin {10}^{0} ) }{2 \: sin {10}^{0} \: cos {10}^{0} }$

$= \dfrac{4 \: \: sin( {30}^{0} - {10}^{0} )}{sin2 \: ( {10}^{0}) }$

$= \dfrac{4 \: \: sin {20}^{0} }{sin {20}^{0} }$

$sin {20}^{0} \: is \: cancel \: out \: from \: numerator \: and \: denominator$

$= 4$