Question

Prove the following identity:sin³ θ+cos³ θ/sin θ+cos θ= 1 – sin θ.cos θ
pls guys ans this question ​

Answer 1

Answer:

LHS = sin^3 A + cos^3 A / sin A + cos A

We know that, a^3+b^3 = (a+b)(a^2+b^2-ab)

Using this formula,

LHS = (sinA+cosA)(sin^2 A + cos^2 A - sin A cos A) / sin A + cos A

= sin^2 A + cos^2 A - sin A cos A

Now we know the identity,

sin^2 A + cos^2 A = 1

So,

LHS = 1- sin A cos A

= RHS

Hence,

LHS = RHS

Hence, proved.