Question

In the given figure, AC = 13cm, BC = 12 cm and ∠B = 90°. Without using tables, find the values of: `("cos A" - "sin A")/("cos A" + "sin A")`

Answer 1

ΔABC is a right-angled triangle.
∴ AC² = AB² + BC²
⇒ AB² 
= AC² - BC²
= 13² - 12²
= 169 - 144
= 25
⇒ AB = 5cm

sin A = `"BC"/"AC" = (12)/(13)`

cos A = `"AB"/"AC" = (5)/(13)`

`("cos A" - "sin A")/("cos A" + "sin A")`

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

= `(-(7)/(13))/((17)/(13)`

= `-(7)/(13) xx (13)/(17)`

= `-(7)/(17)`.