) 187 S -- BSIF® +GEA0 = 1-3Sinke. G

1.	) 187 S -- BSIF® +GEA0 = 1-3Sinke. G
Answer» Using the binomial theorem,(a+b)^3=a^3+3a^2b+3ab^2+b^3 ⇒a^3+b^3=(a+b)^3−3a^2b−3ab^2=(a+b)^3−3(a+b)ab Substitutinga=sin^2(x)aandb=cos^2(x), we have: sin^6(x)+cos^6(x)=(sin^2(x)+cos^2(x))3−3(sin^2(x)+cos^2(x))sin^2(x)cos^2(x) Using the trigonometric identitycos^2(x)+sin^2(x)=1 our expression simplifies to: sin^6(x)+cos^6(x) =1−3sin^2(x)cos^2(x)

Answer»

Using the binomial theorem,(a+b)^3=a^3+3a^2b+3ab^2+b^3

⇒a^3+b^3=(a+b)^3−3a^2b−3ab^2=(a+b)^3−3(a+b)ab

Substitutinga=sin^2(x)aandb=cos^2(x), we have:

sin^6(x)+cos^6(x)=(sin^2(x)+cos^2(x))3−3(sin^2(x)+cos^2(x))sin^2(x)cos^2(x)

Using the trigonometric identitycos^2(x)+sin^2(x)=1 our expression simplifies to:

sin^6(x)+cos^6(x) =1−3sin^2(x)cos^2(x)

Discussion