Question

Prove that question ​

Answer 1

It's too simple dear

a^3 + b^3 = (a+ b) (a^2 + b^2 - ab)

Sin^3x + cos^3x = (sinx + cosx) (Sin^2x + cos^2x - sinx*cosx)

So ,

(Sin^3x + cos^3x) / (sinx + cosx) = ( 1 - sinx*cosx )

(because Sin^2x + cos^2x = 1)

So

(Sin^3x + cos^3x) / (sinx + cosx1) + sinx*cosx = ( 1 - sinx*cosx ) + sinx*cosx = 1

Answered by an IIT JEE ASPIRANT and all India mathematics OLYMPIAD TOPPER in class 10th