How i solve the question of introduction to trigonometry of ncert class 10 of exercise 8.1. Find the easy way to solve this question no.7(1) properly and give me the easiest solution. If cot θ = 7/8, evaluate : (i) (1 + sin θ)(1 – sin θ)/(1+cos θ)(1-cos θ) .
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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 positive real 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 cos function: