Question

If cos A = `3/5`, then find the value of `(sin"A" - cos"A")/(2tan"A")`

Answer 1

cos A = `3/5`

ΔABC

BC² = AC² – AB²

= 5² – 3²

= 25 – 9

= 16

BC = `sqrt(16)` = 4

sin A = `4/5`, tan A = `4/3`

`(sin"A" - cos"A")/(2tan"A") = 4/5 - 3/5 ÷ 2(4/3)`

= `(4 - 3)/5 ÷(8/3)`

= `1/5 xx (3/8)`

= `3/40` 

∴ The value of `(sin"A" - cos"A")/(2tan"A") = 3/40`