Cos^3A+sin^3A/CosA+SinA+Cos^3A-Sin^3A/CosA-SinA=k
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Answer:
LHS:-
=\bold{\frac{(cosA+sinA)(cos^2+sin^2a-sinA.cosA)}{cosA+sinA} +\frac{(cosA-sinA)(sin^2A+cos^2A+sinA.cosA)}{cosA-sinA} }=
cosA+sinA
(cosA+sinA)(cos
2
+sin
2
a−sinA.cosA)
+
cosA−sinA
(cosA−sinA)(sin
2
A+cos
2
A+sinA.cosA)
\begin{lgathered}=\bold{cos^2A+sin^2A-sinA.cosA+sin^2A+cos^2A-sinA.cosA}\\=\bold{1+1}\\=\bold{2=RHS}\end{lgathered}
=cos
2
A+sin
2
A−sinA.cosA+sin
2
A+cos
2
A−sinA.cosA
=1+1
=2=RHS
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