Question

pls help me
if it's right I'll surely mark as brainliest
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Answer 1

$\large\text{\underline{Required}}$

The value of $\dfrac{2\sin A+\tan A}{2\tan A-\sin A}$ if $\sec A=\dfrac{17}{15}$.

$\large\text{\underline{Solution}}$

The main point of the question is the definition of $\sec A$.

$\implies\sec A=\dfrac{1}{\cos A}$

$\large\red{\bigstar}\text{\underline{Tip!}}$

Let's write the function in terms of $\sec A$.

$\implies\text{(Given)}=\dfrac{2\sin A+\tan A}{2\tan A-\sin A}$

$\implies\text{(Given)}=\dfrac{2\sin A+\dfrac{\sin A}{\cos A}}{\dfrac{2\sin A}{\cos A}-\sin A}$

$\implies\text{(Given)}=\dfrac{2+\dfrac{1}{\cos A}}{\dfrac{2}{\cos A}-1}$

$\implies\text{(Given)}=\dfrac{2+\sec A}{2\sec A-1}$

The fraction is in terms of $\sec A$ which value is given as $\dfrac{17}{15}$.

$\implies\text{(Given)}=\dfrac{2+\dfrac{17}{15}}{2\times\dfrac{17}{15}-1}$

$\large\red{\bigstar}\text{\underline{Tip!}}$

What is the value of $\dfrac{15}{15}$? This question may sound easy because the value is $1$. However, we know multiplying 1(a multiplicative identity) to any number does not change the initial value. Now each numerator and denominator gets multiplied $15$.

$\implies\text{(Given)}=\dfrac{30+17}{34-15}$

$\implies\text{(Given)}=\dfrac{47}{19}$

And there is our answer.

$\large\text{\underline{Conclusion}}$

So, the required value is $\dfrac{47}{19}$.

Answer 2

Step-by-step explanation:

solution :

• Sol Given secA =17/15

• E=(2sinA -tanA )/(2 tanA -sinA )

• E=(2sinA - sinA /cosA )/(2sinA /cosA - sinA )

• E=sinA(2 - 1/cosA )/sinA (2/cosA - 1)

• E=(2 - secA )/(2secA -1)

• Putting the value of secA =17/15

• E=(2 - 17/15)/(2×17/15 - 1)

• E=13/19