Question

Simplify (sin^3A+cos^3A)/(sinA+cosA. )+sinA cosA

Answer 1

here is the answer.........

Answer 2

The answer is 1.

Step-by-step explanation:

To simplify: $\frac{(sin^3A+cos^3A)}{(sinA+cosA)}+sinA cosA$

Formula to be used:

• $(a+b)^3 = a^3 +b^3 + 3ab(a+b)$
• $(a+b)^2 = a^2 +b^2 + 2ab$
• $sin^2A+cos^2A =1$

Solution:

$\frac{(sin^3A+cos^3A)}{(sinA+cosA)}+sinA cosA$

$\frac{(sinA + cosA)^3 - 3sinAcosA(sinA+cosA)}{(sinA+cosA)}+sinA cosA$

Taking $(sinA + cosA)$ common

$(sinA + cosA)^2 - 3sinAcosA+sinA cosA$

$(sinA + cosA)^2 - 2sinAcosA$

$sin^2A + cos^2A + 2sinaAcosA - 2sinAcosA$

$sin^2A + cos^2A$

$1$