Question

If 8 tan A = 15, find sin A – cos A.

Answer 1

8 tan A = 15 find. Sin A – cos A

`tan A = 15/8`

tan A = `"Opposite side"/"adjacent side"`

Let x be the hypotenuse By applying theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

𝑥² = 152 + 82

𝑥² = 225 + 64

𝑥² = 289 ⇒ x = 17

`sin A = (AB)/(AC) = 15/17`

`sin A - cos A = 15/17 - 8/17`

`= 7/17`