Question

say answer to this question​

Answer 1

♕$\pink{\large{\underline{\underline{ \rm{Solution }}}}}$♕

$\dfrac{ \sin70 \degree - \cos40 \degree }{ \cos50 \degree - \sin20 \degree }$

➩ $\dfrac{ \sin70 \degree - \sin50 \degree }{ \cos50 \degree - \cos70 \degree }$

➩ $\dfrac{ \sin(60 + 10) - \sin(60 - 10) }{ \cos(60 - 10) - \cos(60 + 10) }$

➩ $\dfrac{ \sin60 \cos10 \: + \: \cos60 \sin10 \: - \: \sin60 \cos10 \: + \: \cos60 \sin10 }{ \cos60 \cos10 \: + \: \sin60\sin10 \: - \: \cos60 \cos10 \: + \: \sin60 \sin 10}$

➩ $\dfrac{ 2 \: \cos60 \sin10} {2 \: \sin60 \sin10 }$

On cutting and Solving, we have:

➩ $\dfrac{ \cos60\degree }{ \sin60\degree }$

We know,

◉ Cos 60° = $\dfrac{1}{2}$

◉ Sin 60° = $\dfrac{ \sqrt{3} }{2}$

Substituting the values, we have:

➩ $\dfrac{ \dfrac{1}{2} }{ \dfrac{ \sqrt{3} }{2} }$

➩ $\dfrac{1}{2} \times \dfrac{2}{ \sqrt{3} }$

➩ $\green { \underline{ \boxed { \frac{1}{ \sqrt{3} }}}}$

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