Question

sin3theta + cos3theta / sintheta + cos theta = 1 - sintheta . costheta​

Answer 1

Here, we need to know that

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

Answer 2

Step-by-step explanation:

$\frac{ { \sin(θ) }^{3} + { \ \cos(θ) }^{3} }{\sin(θ) + \ cos (θ)} \: = \frac{{\sin^{2} (θ) + \ cos ^{2} (θ)( \: \sin(θ)cos (θ))}}{sin(θ) + \ cos (θ)}$

= $\frac{(sin(θ) + \ cos (θ))(1 - \: sin(θ) cos (θ))}{ \: sin(θ) + \ cos (θ) }$

= $1 - sin(θ)cos (θ)$