Question

simplify: (secA+tanA)(1-sinA)

Answer 1

(secA+tanA)(1-sinA)

=>secA(1-sinA)+tanA(1-sinA)

=>secA-secAsinA+tanA-tanAsinA

=>secA - sinA/cosA +tanA - sinA/cosA×sinA

=>secA - tanA + tanA - sin²A/cosA

=>secA - sin²A/cosA

=>secA - sin²AsecA

=>secA(1-sin²A)

=>secA×cos²A

=>cosA

So, (secA+tanA)(1-sinA) = cosA

Cheers!

Answer 2

To Simplify

→ (secA + tanA)(1 - sinA)

Solution

→ (secA + tanA)(1 - sinA)

→ (1/cosA + sinA/cosA)(1 - sinA)

→ (1 + sinA)/cosA × (1 - sinA)

→ (1 + sinA)(1 - sinA)/cosA

→ (1² - sin²A)/cosA

→ (1 - sin²A)/cosA

→ cos²A/cosA

→ cosA

Answer: cosA

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Identities used

• (a + b)(a - b) = a² - b²
• sec∅ = 1/cos∅
• tan∅ = sin∅/cos∅
• 1 - sin²∅ = cos²∅