Question

In TABC, +B = 90º, BC = 5 cm, AC − AB = 1, What wiil be the value of cos sin C C 1 1 + + ?

Answer 1

Answer:

We have a ∆ABC where angle B = 90°

and BC = 5 cm also AC - AB = 1...(1)

Now applying Pythagoras theorem we get,

AB²+BC²=AC²

or, BC²= AC²- AB²

or, (BC)²= (AC-AB)(AC+AB)

or, (5)²= 1×(AC+AB)

or, 25 = AC + AB...(2)

Now adding equation (1) and (2) we get,

2AC = 26

or, AC = 13 cm

So, sinC = 12/13 and cosC = 5/13

Now,$\frac{1 + \sin(c) }{1 + \cos(c) 1+cos(c)1+sin(c)$

= {1+(12/13)}/1+(5/13)}

= (25/13)/(18/13)

= 25/18

That's it

Hope it helped (*^_^*)