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Svetradugi [14.3K]
3 years ago
5

Please help... I have no clue

Mathematics
1 answer:
muminat3 years ago
5 0

Answer:

OPTION C:  Sin C - Cos C = s - r

Step-by-step 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 = \frac{opp}{hyp} = \frac{AC}{BC} = \frac{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 = \frac{adj}{hyp} = \frac{AB}{BC} = \frac{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 = \frac{opp}{hyp} $

⇒  $ Sin C = \frac{AB}{BC} $

              $ = \frac{sh}{h} $

               = s

Sin C = s

$  Cos C = \frac{adj}{hyp} $

$ \implies Cos C = \frac{AC}{BC} $

⇒ Cos C = $ \frac{rh}{h} $

Therefore, Cos C = r

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

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