Q) If cot θ =7/8, then find the value of (1+sin θ)(1−sin θ)/(1+cos θ)(1−cos θ).

(Q 22 B – 30/1/3 – CBSE 2026 Question Paper)

Ans: 

Step 1: Let’s first simiplify the given expression:

= ………… (i)

Step 2: From Trigonometric identity, we know that

sin ² θ + cos ² θ = 1

∴ 1 – sin ² θ = cos ² θ ………… (ii)

and 1 – cos ² θ = sin ² θ ………… (iii)

Step 3: Substituting the values from equation (ii) and (iii), we get:

=

= cot ² θ

Step 4: ∵ We are given that cot θ = 7/8

∴ cot ² θ = (cot θ) ² =

Therefore, the value of given expression is .

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