Question

Please help... I have no clue

Answer 1

OPTION C: Sin C - Cos C = s - r

Explanation:

ABC is a right angled triangle. ∠A = 90°, from the figure.

Therefore, BC = hypotenuse, say h

Now, we find the length of AB and AC.

We know that:
`$ \textbf{Sin A} = \frac{\textbf{opp}}{\textbf{hyp}} $`

and
`$ \textbf{Cos A} = \frac{\textbf{adj}}{\textbf{hyp}} $`

Given, Sin B = r and Cos B = s

⇒
`$ Sin B = r = (opp)/(hyp) = (AC)/(BC) = (AC)/(h) $`

⇒
`$ \textbf{AC} = \textbf{rh} $`

Hence, the length of the side AC = rh

Now, to compute the length of AB, we use Cos B.

`$ Cos B = s = (adj)/(hyp) = (AB)/(BC) = (AB)/(h) $`

⇒
`$ \textbf{AB} = \textbf{sh} $`

Hence, the length of the side AB = sh

Now, we are asked to compute Sin C - Cos C.

`$ Sin C = (opp)/(hyp) $`

⇒
`$ Sin C = (AB)/(BC) $`

`$ = (sh)/(h) $`

= s

Sin C = s

`$ Cos C = (adj)/(hyp) $`

`$ \implies Cos C = (AC)/(BC) $`

⇒ Cos C =
`$ (rh)/(h) $`

Therefore, Cos C = r

So, Sin C - Cos C = s - r, which is OPTION C and is the right answer.