Prove \sin^3 A−\cos^3 A=(\sin^2 A−\cos^2 A)(1-2\sin^2 A \cos^2 A)

2alr8w

2alr8w

Answered question

2022-01-25

Prove sin3Acos3A=(sin2Acos2A)(12sin2Acos2A)

Answer & Explanation

Howard Gallagher

Howard Gallagher

Beginner2022-01-26Added 13 answers

Hint:
sin3Acos3A=sin3Asin2AcosA+sin2AcosAsinAcos2A+sinAcos2Acos3A
=sin2A(1cosA)+sinAcosA(sinAcosA)cos2A(1sinA)
tsjutten20

tsjutten20

Beginner2022-01-27Added 13 answers

With x=π the LHS is equal to 1 while the RHS is equal to -1 therefore the identity is false.

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