Question

In triangle ABC <B=90, BC = 5cm , Ac-AB = 1 ,evaluate 1+sinc/1+cosc

Answer 1

I think it helps you

Answer 2

Trigonometry,

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

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

= 25/18

That's it
Hope it helped (*^_^*)