Prove v(3cosx+4sinx)2+(4cosx-3sinx)2 = 5

Question

Proving Basic Problems: I have to prove that one side equals the other using identities.

 

√(3cosx+4sinx)2+(4cosx-3sinx)² = 5

 

Please show the steps or even try to explain the process to me! :)

Answer 1

Expand each square term:

 

SQRT [(9cos²x + 24sinxcosx + 16sin²x)+(16cos²x -24sinxcosx + 9sin²x)]

 

Combine like terms

 

SQRT (25cos²x +25sin²x)

 

SQRT (25(cos²x + sin²x)

 

SQRT 25 = 5