Question

solve this question​

Answer 1

(Instead of θ, I use A)

Answer: 2

Step-by-step explanation:

Given : To find the value of $\frac{Cos^3A + Sin^3A}{CosA+SinA} + \frac{Cos^3A - Sin^3A}{CosA - SinA}$

Solution :

⇒ $\frac{Cos^3A + Sin^3A}{CosA+SinA} + \frac{Cos^3A - Sin^3A}{CosA - SinA}$

We know that,

a³ - b³ = ( a - b ) ( a² + ab + b² )

a³ + b³ = ( a + b ) ( a² - ab + b² )

Substituting a = Cos A , b = Sin A

We get,

⇒ $\frac{(CosA + SinA)(Cos^2A - SinACosA + Sin^2A}{CosA + SinA} + \frac{(CosA - SinA)(Cos^2A + SinACosA + Sin^2A)}{CosA - SinA}$

⇒ $( Cos^2A - SinACosA + Sin^2A ) + ( Cos^2A + SinACosA + Sin^2A )$

⇒ $2 Cos^{2} A + 2 Sin^2A = 2(Sin^{2} A + Cos^2A) = 2(1) = 2$  

∴  $Sin^2A + Cos^2A = 1$

_____________________________

                         Hope it Helps!!