Math, asked by sharmagiana0, 5 months ago

if tan a=3/4 then find the value a(sina-cosa)/a (sina +cos a)

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Answered by Anonymous
7

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Answered by Syamkumarr
0

Answer:

The correct answer is -\frac{1}{7}  

Step-by-step explanation:

Given data  

in a right angle triangle  tan a = \frac{3}{4}  

then here we need to find  \frac{ a(sin a -cos a )}{ a ( sin a + cos a) }    

we know that tanθ = opposite side / hypotenuse  

\frac{3}{4}  = \frac{opposite side }{ adjacent side }  

⇒ opposite side = 3 and adjacent side = 4

⇒ from Pythagoras theorem  in a right angle triangle

⇒ hypotenuse²  = side² + side²  

                           = 3²  + 4²  = 9 + 16 = 25

                           = 5²  

     hypotenuse  = 5              

⇒ in the triangle,

 opposite side = 3, adjacent side = 4 and hypotenuse = 5

⇒ sin a = \frac{opposite side}{hypotenuse} = \frac{3}{5}            cos a = \frac{ adjacent side }{hypotenuse } = \frac{4}{5}  

given problem \frac{a (sin a - cos a)}{a (sin a + cos a)}

                       =  \frac{sin a - cos a }{sin a + cos a}  

                       = \frac{ \frac{3}{5} - \frac{4}{5}  }{\frac{3}{5} + \frac{4}{5}  } = (- 1/5)/ (7/5) = -1 /7    

               

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