The Total solution for NCERT class 6-12
If cot ╬╕ = 7/8,evaluate :
(i) (1 + sin ╬╕)(1 тАУ sin ╬╕)/(1+cos ╬╕)(1-cos ╬╕)
Solution:
Let┬аus assume a тЦ│ABC┬аin which┬атИаB = 90┬░ and тИаC = ╬╕
Given:
cot ╬╕ = BC/AB = 7/8
Let BC = 7k and AB = 8k, where k is a positivereal number
According to Pythagoras theorem in┬атЦ│ABC┬аwe get.
AC2┬а= AB2+BC2
AC2┬а= (8k)2+(7k)2
AC2┬а= 64k2+49k2
AC2┬а= 113k2
AC = тИЪ113 k
According to the sine and cos function ratios,it is written as
sin ╬╕ = AB/AC = Opposite Side/Hypotenuse =8k/тИЪ113 k = 8/тИЪ113 and
cos ╬╕ = Adjacent Side/Hypotenuse = BC/AC =7k/тИЪ113 k = 7/тИЪ113
Now apply the values of sin function and cosfunction: