Question

if 5 tan theta =4 tan 45 degree find the value of 5sin theta - 3 cos theta/5 sin theta +2cos theta

Answer 1

Step-by-step explanation:

thetha ki jagah@ likh raha hu

5tan@=4 tan45⁰

5tan@= 4 ( u know tan45=1)

tan@=4/5=p/b

h²=p²+b²

h²=4²+5²

h²=16+25=41

h=√41

sin@=p/h=4/√41

cos@=b/h=5/√41

put these values in eq u will get right answer

Answer 2

$\boxed{ \underline {\sf {\green{Given :-}}}} \\ \\ \bold{5 \tan \theta \: = 4 } \\ \implies{ \tan \theta \: = \: \frac{4}{5} \: \: \: \: \: \: \: \: \: \: \: ....(i) } \\ \\ \boxed{ \underline {\sf {\green{solution :-}}}} \\ \bold{Now,} \\ \\ \sf \implies{ \frac{5 \sin \theta - 3 \cos \theta }{5 \sin \theta + 2 \cos \theta } = \frac{5 \frac{ \sin \theta }{ \cos\theta } - 3 \frac{ \cos \theta}{ \cos\theta} }{5 \frac{ \sin\theta}{ \cos\theta } + 2 \frac{ \cos\theta}{ \cos\theta} } } \\ \\ \: \: \: \: \: \: \: \: \: \: \sf[Divide \: the \: numerator \: and \: denominator \: by \: cos \theta] \\ \\ \sf \implies{ \frac{5 \tan \theta - 3 }{5 \tan \theta + 2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (∵ \: \tan \theta \: = \frac{ \sin \theta }{ \cos \theta }) } \\ \\ \sf \implies{ \frac{5 . \frac{4}{5} - 3 }{5. \frac{4}{5} + 2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [ \: using \: (i) \: ]} \\ \\ \sf \purple{ \implies{\frac{4 - 3}{4 + 2} = \frac{1}{6} .}}$