Question

If tan theta=4 the value of 7sintheta _3cos theta/7sin theta + 3cos theta is dash

Answer 1

Answer:

The value of given Trigonometrical expression for the TanФ = 4 is  $\dfrac{25}{31}$ .

Step-by-step explanation:

Given as :

The trigonometrical expression as

$\dfrac{7 sin\Theta - 3 cos\Theta }{7 sin\Theta + 3 cos\Theta }$

And The value of TanФ = 4

Now, Divide the numerator and denominator by cosФ in given expression

So, $\dfrac{\dfrac{7 sin\Theta - 3 cos\Theta }{cos\Theta }}{\dfrac{7 sin\Theta + 3 cos\Theta }{cos\Theta }}$

∵ TanФ = $\dfrac{sin\Theta }{cos\Theta }$

So, The expression can be written as

$\dfrac{7 Tan\Theta - 3}{7 Tan\Theta + 3}$

Now, putting the value of TanФ = 4 ,we get

$\dfrac{7 \times 4 - 3}{7 \times 4 + 3}$

Or, $\dfrac{28 - 3}{28 + 3}$

i.e $\dfrac{25}{31}$

Hence , The value of given Trigonometrical expression for the TanФ = 4 is  $\dfrac{25}{31}$ . Answer