The Total solution for NCERT class 6-12
If cot θ = 7/8,evaluate :
(i) (1 + sin θ)(1 – sin θ)/(1+cos θ)(1-cos θ)
Solution:
Let us assume a △ABC in which ∠B = 90° and ∠C = θ
Given:
cot θ = BC/AB = 7/8
Let BC = 7k and AB = 8k, where k is a positivereal number
According to Pythagoras theorem in △ABC we get.
AC2 = AB2+BC2
AC2 = (8k)2+(7k)2
AC2 = 64k2+49k2
AC2 = 113k2
AC = √113 k
According to the sine and cos function ratios,it is written as
sin θ = AB/AC = Opposite Side/Hypotenuse =8k/√113 k = 8/√113 and
cos θ = Adjacent Side/Hypotenuse = BC/AC =7k/√113 k = 7/√113
Now apply the values of sin function and cosfunction: