Question

Prove the identity :
sin³0+ cose³0/sin0+cos0=1 - sin 0 cos 0​

Answer 1

Answer:

Step-by-step explanation:

sin³ θ+ cos³ θ/sin θ+cos θ = 1 - sin θ.cos θ;

[​(sin θ+ cos θ){sin² θ - sin θ. cos θ + cos² θ}] / (sin θ+cos θ) = 1 - sin θ.cos θ;         (since, a³ + b³ = (a + b)(a² - ab + b²))

{sin² θ - sin θ. cos θ + cos² θ} = 1 - sin θ.cos θ;  

sin² θ - sin θ. cos θ + cos² θ + sin θ.cos θ= 1 ;

sin² θ + cos² θ = 1;

1 = 1;                                                    (Since,  sin² θ + cos² = 1)

Thus, LHS = RHS.    

That's all.

Answer 2

Step-by-step explanation:

Step-by-step explanation:

sin³ 0+ cos³ 0/sin 0+cos 0 = 1 - sin 0.cos e;

[(sin 0+ cos 0){sin² 0 - sin 0. cos 0 + cos² 0}] / (sin e+cos 0) = 1 - sin 0.cos 0; (since, a³ + b³ = (a + b)(a² - ab + b²)) 3

{sin² 0 - sin 0. cos 0 + cos² 0} = 1 - sin 0.cos 0;

sin² 0 - sin 0. cos 0 + cos² 0 + sin 0.cos 0= 1;

sin² 0 + cos² 0 = 1;

1 = 1;

(Since, sin² 0 + cos² = 1)

Thus, LHS = RHS.