Question

If `sin θ = 3/5`, evaluate `((cos θ - 1/(tan θ)))/(2 cot θ)`.

Answer 1

We have

`sin θ = 3/5`

In ΔABC

AC² = AB² + BC²

⇒ (5)² = (3)² + (BC)²

⇒ 25 = 9 + (BC)²

⇒ (BC)² = 25 – 9

⇒ (BC)² = 16

⇒ BC = 4

∴ `cos θ = 4/5` and `cot θ = 4/3`

Now `(cos θ - 1/(tan θ))/(2 cot θ) = ((4/5) - (4/3))/(2 xx 4/3)`

= `((12  -  20)/15)/(8/3)`

= `(-8)/15 xx 3/8`

= `(-1)/5`