Question

Express 2 cos4x sin2x as an algebraic sum of sines and cosines.

Answer 1

$\textbf{\underline{Answer :}}$

We know that,

sin(A + B) = sinA cosB + cosA sinB

sin(A - B) = sinA cosB - cosA sinB

Adding, we get

sin(A + B) + sin(A - B) = 2 sinA cosB

So, we deduce a formula :

2 sinA cosB = sin(A + B) + sin(A - B)

Now,

2 cos4x sin2x

= 2 sin2x cos4x

= sin(2x + 4x) + sin(2x - 4x)

= sin6x + sin(- 2x)

= sin6x + cos(90 + 2x),

which is the required Algebraic sum.

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Answer 2

Answer:

2 =(+) +(-)

(6+4) +(6-4)

10+2