Question

If cottheta= 7/8,evaluate (1+sin theta)(1-sin theta)/(1+costheta)(1-cos theta)​

Answer 1

Answer

Given, cot θ = 7/8

=> tan θ = 1/(7/8) {since tan θ = 1/cot θ}

=> tan θ = 8/7

In the figure,

from triangle ABC,

Apply Pythagoras Theorem, we get

=> (Hypotanous)2 = (Perpendicular)2 + (Base)2

=> AC2 = AB2 + BC2

=> AC2 = 82 + 72

AC2 = 64 + 49

=> AC2 = 113

=> AC = √113

Given, {(1 + sin θ)*(1 - sin θ)}/{(1 + cos θ)*(1 - cos θ)}

= (1 - sin2 θ)}/{(1 - cos2 θ) {since a2 - b2 = (a - b)*(a + b)}

= (1 - sin2 θ)}/sin2 θ {since sin2 θ + cos2 θ = 1 }

Grom the figure, sin θ = AB/AC = 8/√113

Now, (1 - sin2 θ)}/sin2 θ = {1 - (8/√113)2 )}/(8/√113)2

= (1 - 64/113)/(64/113)

= {(113 - 64)/113}/(64/113)

= (49/113)/(64/113)

= 49/64

Hence, {(1 + sin θ)*(1 - sin θ)}/{(1 + cos θ)*(1 - cos θ)} = 49/64

Answer 2

Step-by-step explanation:

This is the answer

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