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If cot θ = 7/8, evaluate : (i) (1 + sin θ)(1 – sin θ)/(1+cos θ)(1-cos θ) . Q.7(1)

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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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  1. 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:

    Ncert solutions class 10 chapter 8-2

     

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