Question

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

Answer 1

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Answer 2

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