If tan⁡A=$$\frac{8}{15}$$​ then find sinA+cosA.

Correct option is C

Given:

We are given that:
​$$\tan A = \frac{8}{15}$$​​
We need to find the value of sin A + cos A .

Solution

Step 1: Using the Pythagorean identity to find sin A and cos A :
Given tan $$A = \frac{8}{15}$$​ , we can think of this as a right triangle where the opposite side is 8 and the adjacent side is 15.
Using the Pythagorean theorem, we find the hypotenuse h :

​$$h = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$$​​

Now, we can find sin A and cos A :

​$$sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{17}\\cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{17}$$​​

Then the value of sin A + cos A :

​$$\sin A + \cos A = \frac{8}{17} + \frac{15}{17} = \frac{8 + 15}{17} = \frac{23}{17}$$​​