Question

If 5 cos A – 12 sin A = 0, evaluate without using tables `(sin A + cos A)/(2 cos A - sin A)`.

Answer 1

Given: 5 cos A – 12 sin A = 0; find `(sin A + cos A)/(2 cos A - sin A)`.

Step-wise calculation:

1. Rearrange:

5 cos A = 12 sin A 

⇒ `tan A = (sin A)/(cos A)`

= `5/12`

2. Take a right triangle with opposite = 5, adjacent = 12, hypotenuse = `13 (sqrt(5^2 + 12^2))` = 13. 

Thus, `sin A = 5/13` and `cos A = 12/13`.

3. Numerator:

sin A + cos A 

= `5/13 + 12/13`

= `17/13`

4. Denominator:

2 cos A – sin A 

= `2 (12/13) - (5/13)`

= `(24 - 5)/13`

= `19/13`

5. Ratio:

`17/13 ÷ 19/13` 

= `17/19`