Question

if 5 tan theta minus 4 is equal to zero . find the value of 5 sin theta + 4 cos theta by 5 cos theta minus sin theta​

Answer 1

Step-by-step explanation:

ans is 40/21

hope this helped...

Answer 2

AnswEr :

$\bold{we \: have} \begin{cases} \sf{Given:5 \tan( \theta) - 4 = 0 } \\ \\ \sf{To \: Find : \dfrac{5 \sin(\theta) + 4 \cos(\theta) }{5 \cos(\theta) - \sin(\theta) } } \end{cases}$

• According to the Given Statement :

⇒ 5 tan(θ) - 4 = 0

⇒ 5 tan(θ) = 4

⇒ tan(θ) = $\sf\dfrac{4}{5}$

_________________________________

• Let's Head to the Question Now :

$\Longrightarrow \rm\dfrac{5 \sin(\theta) + 4 \cos(\theta) }{5 \cos(\theta) - \sin(\theta)}$

⠀⠀⠀⠀⋆ Dividing Each term by cos(θ)

$\Longrightarrow \rm\dfrac{ \dfrac{5 \sin(\theta)}{\cos(\theta)} + \dfrac{4 \cancel{\cos(\theta)}}{ \cancel{\cos(\theta)}} }{ \dfrac{5 \cancel{\cos(\theta)}}{ \cancel{\cos(\theta)}} - \dfrac{ \sin(\theta)}{\cos(\theta)}}$

$\Longrightarrow \rm\dfrac{ \dfrac{5 \sin(\theta)}{\cos(\theta)} + 4 }{ 5 - \dfrac{\sin(\theta)}{\cos(\theta)}}$

⠀⠀⠀⠀⋆ sin(θ) / cos(θ) = tan(θ)

$\Longrightarrow \rm\dfrac{5 \tan( \theta) + 4 }{ 5- \tan(\theta)}$

$\Longrightarrow \rm\dfrac{ \bigg( \cancel5 \times \dfrac{4}{ \cancel5} \bigg) + 4 }{\bigg(5 - \dfrac{4}{ 5}\bigg)}$

$\Longrightarrow \rm\dfrac{ 4 + 4}{ \dfrac{21}{5} }$

$\Longrightarrow \rm\dfrac{8 \times 5}{21}$

$\Longrightarrow \large \boxed{ \rm \dfrac{40}{21} }$

⠀

$\therefore \boxed{\dfrac{5 \sin(\theta) + 4 \cos(\theta) }{5 \cos(\theta) - \sin(\theta) } = \dfrac{40}{21} }$