Question

prove cos3Acos2A+sin4AsinA=cosAcos2A

Answer 1

Answer:

Step-by-step explanation:

The given equation is:

$cos3Aco2A+sin4AsinA=cosAcos2A$

Taking the LHS of the above equation and multiplying throughout with 2, we get

$2cos3Acos2A+2sin4AsinA$

⇒$cos(3A+2A)+cos(3A-2A)+cos(4A-A)-cos(4A+A)$

⇒$cos5A+cosA+cos3A-cos5A$

⇒$cosA+cos3A$

Now, RHS=$cosAcos2A$

Multiplying by 2, we get

$2cosAcos2A$

⇒$cos(A+2A)+cos(A-2A)$

⇒$cos3A+cosA$

Hence LHS=RHS.