Question

1+sina)(1+cosa)=5/4 then the value of (1-sina)(1-cosa) is equal to

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Answer 1

Answer:

Given that ;

(1 + sinα)(1 + cosα) = $\sf \dfrac{5}{4}$

On multiplying both sides by (1 - sinα)(1 - cosα)

⇒ {(1 + sinα)(1 + cosα)}{(1 - sinα)(1 - cosα)} = $\sf \dfrac{5}{4}$ * (1 - sinα)(1 - cosα)

⇒ (1 - sin²α)(1 - cos²α) = $\sf \dfrac{5}{4}$ * (1 - sinα)(1 - cosα)

⇒ cos²α * sin²α = $\sf \dfrac{5}{4}$ * (1 - sinα)(1 - cosα)

⇒ (1 - sinα)(1 - cosα) = $\sf \dfrac{4}{5}$ ( cos²α sin²α )

$\rule{300}{2}$

Important identities used-

• 1 - sin²θ = cos²θ
• 1 - cos²θ = sin²θ
• (a + b)(a - b) = a² - b²