Simplify the following (sin³A - cos³ A)/(sin A - cos A) , where A is an acute angle.

Simplify the following (sin³A - cos³ A)/(sin A - cos A)…

Simplify the following $\frac{sin^3A - cos^3 A}{sin A - cos A}$ , where A is an acute angle.

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 1 + sinA cosA.

⇒ $\frac{sin^3A - cos^3 A}{sin A - cos A}$

We know that,

⇒ (a³ - b³) = (a - b)(a² + b² + ab)

Now,

$\frac{sin^3A - cos^3 A}{sin A - cos A}$ = $\frac{(sinA - cosA)(sin^2A + cos^2A + sinA cosA)}{(sinA-cosA)}$

⇒ sin²A + cos²A + sinA cosA

⇒ 1 + sinA cosA [sin²A + cos²A = 1]