Question

If cot =7/8
evaluate : (i)
(1 + sin 0) (1 - sin o)/
(1 + cos 0) (1 - cos)
(ii) cote​

Answer 1

Answer:

cotθ = 49/64

Step-by-step explanation:

To find (i):

$\Longrightarrow \sf \dfrac{(1+sin\theta)(1-sin\theta)}{(1+cos\theta)(1-cos\theta)}$

⇒ Using (a - b)(a + b) = a² - b² we get,

$\Longrightarrow \sf \dfrac{1^2-sin^2\theta}{1^2-cos^2\theta}$

⇒ Using 1 - sin²θ = cos²θ and  1 - cos²θ = sin²θ we get,

$\Longrightarrow \sf \dfrac{cos^2\theta}{sin^2\theta}$

⇒ Using cos²θ/sin²θ = cot²θ we get,

$\Longrightarrow \sf cot^2\theta$

⇒ Using cotθ = 7/8 we get,

$\Longrightarrow \sf \left(\dfrac{7}{8}\right)^2$

$\Longrightarrow \sf \dfrac{49}{64}$

Therefore,

$\Longrightarrow \sf \dfrac{(1+sin\theta)(1-sin\theta)}{(1+cos\theta)(1-cos\theta)} = \dfrac{49}{64}$

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To find (ii): cot²θ

$\Longrightarrow \sf \left(\dfrac{7}{8}\right)^2$

$\Longrightarrow \sf \dfrac{49}{64}$