Simplify the following.

$$\frac{sin^3\alpha + cos^3\alpha }{sin \alpha + cos\alpha}$$​

Correct option is C

Given: 

$$\frac{sin^3\alpha + cos^3\alpha }{sin \alpha + cos\alpha}$$ 

Formula Used: 

$$sin^2 \theta + cos^2 \theta$$ = 1  

$$a^3 + b^3 = (a+b)(a^2 +b^2 -ab)$$​

Solution:

$$\frac{sin^3\alpha + cos^3\alpha }{sin \alpha + cos\alpha}$$​​

= $$\frac{(sin\alpha + cos\alpha )(sin ^2 \alpha + cos^2 \alpha -sin \alpha cos \alpha)}{(sin\alpha + cos\alpha )}$$ 

= 1 - $$sin\alpha.cos\alpha$$​