Question

if 5tan thitha =12,find the valie of 2cos thitha +sin thitha/ sin thitha - cos thitha​

Answer 1

Given :

$\star \: 5\tan \theta = 12 \\ \\ \star \: \tan \:\theta = \dfrac{12}{5}$

To find :

$\star \: \dfrac{2 \cos\theta + \sin\theta}{ \sin\theta - \cos\theta}$

Solution :

$\implies \: \dfrac{2 \cos\theta + \sin\theta}{ \sin\theta - \cos\theta}$

Here , Divide both numerator and denominator by cos@ .

$\implies \: \dfrac{ \dfrac{2 \cos\theta + \sin\theta}{ \cos\theta} }{ \dfrac{ \sin\theta - \cos\theta}{ \cos\theta} } \\ \\ \implies \: \dfrac{2 + \tan\theta}{ \tan\theta - 1}$

Now , put the value of tan@ = 12/5 .

$\implies \: \dfrac{2 + \dfrac{12}{5} }{ \dfrac{12}{5} - 1 } \\ \\ \implies \: \dfrac{ \dfrac{10 + 12}{ \cancel5} }{ \dfrac{12 - 5}{ \cancel5} } \\ \\ \implies \: \: \dfrac{22}{7}$

Hence , the value is 22/7 .

Answer 2

Answer:

$Given :</p><p></p><p>\begin{lgathered}\star \: 5\tan \theta = 12 \\ \\ \star \: \tan \:\theta = \dfrac{12}{5}\end{lgathered}⋆5tanθ=12⋆tanθ=512</p><p></p><p>To find :</p><p></p><p>\begin{lgathered}\star \: \dfrac{2 \cos\theta + \sin\theta}{ \sin\theta - \cos\theta} \\\end{lgathered}⋆sinθ−cosθ2cosθ+sinθ</p><p></p><p>Solution :</p><p></p><p>\begin{lgathered}\implies \: \dfrac{2 \cos\theta + \sin\theta}{ \sin\theta - \cos\theta} \\\end{lgathered}⟹sinθ−cosθ2cosθ+sinθ</p><p></p><p>Here , Divide both numerator and denominator by cos@ .</p><p></p><p>\begin{lgathered}\implies \: \dfrac{ \dfrac{2 \cos\theta + \sin\theta}{ \cos\theta} }{ \dfrac{ \sin\theta - \cos\theta}{ \cos\theta} } \\ \\ \implies \: \dfrac{2 + \tan\theta}{ \tan\theta - 1} \\\end{lgathered}⟹cosθsinθ−cosθcosθ2cosθ+sinθ⟹tanθ−12+tanθ</p><p></p><p>Now , put the value of tan@ = 12/5 .</p><p></p><p>\begin{lgathered}\implies \: \dfrac{2 + \dfrac{12}{5} }{ \dfrac{12}{5} - 1 } \\ \\ \implies \: \dfrac{ \dfrac{10 + 12}{ \cancel5} }{ \dfrac{12 - 5}{ \cancel5} } \\ \\ \implies \: \: \dfrac{22}{7}\end{lgathered}⟹512−12+512⟹512−5510+12⟹722</p><p></p><p>Hence , the value is 22/7 .</p><p></p><p>$