Question

Cos^3a-sin^3a/cosa-sina

Answer 1

Answer:

1 + cosa sina

Step-by-step explanation:

$\frac{cos^3a-sin^3a}{cosa-sina}$

cos³a - sin³a ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

cos³a - sin³a

= (cosa - sina )(cos²a + cosa sina + sin²a)

= (cosa - sina)(1 + cosa sina) [ sin²a + cos²a = 1 ]

Then

$\frac{cos^3a-sin^3a}{cosa-sina}$

= $\frac{(cosa-sina)(1+cosasina)}{cosa-sina}$ ← cancel (cosa - sina) on numerator/ denominator

= 1 + cosa sina