Math, asked by ranimittakolu17, 4 months ago

if tan theta=3 , then what is the value of [5sintheta-3costheta/4sintheta+3costheta] ?
please answer me fast

Answers

Answered by OfficialPk
0

Answer:

Answer:

tan = 3

if ABC is a right angeled triangle and right angled at B

so tan = \frac{opposite \: side}{Adjacent \: Side}

tan = \frac{3}{1}

from the value of tan

AB = 3

BC = 1

AC = ?

From \: pythagores \: Thereom

{AC}^{2}={AB}^{2}+{BC}^{2}

{AC}^{2}={3}^{2}+{1}^{2}

{AC}^{2} = 9+1=10

{AC}= \sqrt{10}

From the above values

sin = AB/AC

sin =

 \frac{3}{ \sqrt{10} }

cos = BC/AC

cos =

 \frac{1}{ \sqrt{10} }

so

5 sin - 3 cos / 4 sin + 3 cos

 =  \frac{5 \times  \frac{3}{ \sqrt{10} }  - 3 \times  \frac{1}{ \sqrt{10} } }{4 \times  \frac{3}{ \sqrt{10} }  + 3 \times  \frac{1}{ \sqrt{10} }  } \\  =  \frac{ \frac{15}{ \sqrt{10}  }  -  \frac{3}{ \sqrt{10} } }{ \frac{12}{ \sqrt{10} } +  \frac{3}{10}  }  \\  =  \frac{ \frac{15 - 3}{ \sqrt{10} } }{ \frac{12 + 3}{ \sqrt{10} } }  \\  =  =  >  \frac{12}{15}  =  \frac{4}{5}

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