Question

sec A (1_sin A)(1_sin A)(sceA+tan A
$sec(1 - \sin a) ( sec a +tan a)$
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Answer 1

Solution

→ secA(1 - sinA)(secA + tanA)

We know secA = 1/cosA and tanA = sinA/cosA.

→ 1/cosA × (1 - sinA)(1/cosA + sinA/cosA)

→ 1/cosA × (1 - sinA)(1 + sinA)/cosA

Since (1 - sinA)(1 + sinA) = 1² - sin²A.

→ 1/cosA × (1 - sin²A)/cosA

We know that 1 - sin²A = cos²A

→ 1/cosA × cos²A/cosA

→ cos²A/cos²A = 1

Hence required answer is 1.