Question

In triangle ABC, angleB=90,BC=5cm,AC-AB=1,evaluate: 1+SinC/1+cosC

Answer 1

Answer:

25/18   or     1.388889 (approx)

Step-by-step explanation:

ABC is a right angled triangle at B.

BC= 5 cm ,

AC-AB=1

AC=1+AB    --(1)

In Triangle ABC .

By Pythagoras theorem

AC^{2} = AB^{2}  + BC ^{2}

from (1)

(1+AB)^{2} = AB^{2} + 5^{2}

1 + AB^{2} + 2 AB = AB^{2} + 25

1 + 2 AB = 25

2 AB = 25 - 1

AB = 24/2

AB = 12 cm

AC - AB = 1

AC = 1 + AB

AC = 1 + 12

AC = 13 cm

1 + sin C/1 + cos C  

sin C = AB/AC = 12/13

cos C = BC/AC = 5/13

1 + 12/13    /    1 + 5/13

13 + 12/13    /    13 + 5/13

25/13   /    18/13

25/18

Hence proof