Math, asked by amrl24041977, 10 months ago

If 5 tan theta is equal to 4 then find the value of 5 theta minus 3 cos theta upon 5 sin theta + 2 cos theta

Answers

Answered by AkshitSaxena333
1

Step-by-step explanation:

here us the answer buddy.. do let me know if this was helpful

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Answered by Anonymous
1

 \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} .}}

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