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

Question

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)

Sapling Academy · Accepted Answer

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

$\frac{(1+\sin 	heta)(1 - \sin 	heta)}{(1+\cos 	heta)(1 - \cos 	heta)}$

= $\frac{(1-\sin^2 	heta)}{(1 - \cos^2 	heta)}$ ............ (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:

$\frac{(1-\sin^2 	heta)}{(1 -\cos^2 	heta)}$

= $\frac{(\cos^2 	heta)}{(\sin^2 	heta)}$

= cot 2 θ

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

∴ cot 2 θ = (cot θ) 2 = $(\frac{7}{8})^2 = \frac{49}{64}$

Therefore, the value of given expression is $\frac{49}{64}$.

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