Question

4sina*cosa*(cos²a-sin²a)​

Answer 1

$\underbrace {4\, sina\cdot cosa}_{2\cdot sin2a}\cdot (\underbrace {cos^2a-sin^2a}_{cos2a})=2\cdot sin2a\cdot cos2a=sin4a\\\\\\\star \; \; 2\cdot sinx\cdot cosx=sin2x\; \; \star \\\\\star \; \; cos^2x-sin^2x=cos2x\; \; \star$

Answer 2

To simplify the expression 4sin(a)cos(a)(cos^2(a)-sin^2(a)), we can use trigonometric identities. Let's break it down step by step:

First, let's apply the identity cos^2(a) - sin^2(a) = cos(2a):

4sin(a)cos(a)(cos^2(a)-sin^2(a)) = 4sin(a)cos(a)cos(2a)

Next, we can use the double-angle identity for sine, which states that sin(2a) = 2sin(a)cos(a):

4sin(a)cos(a)cos(2a) = 4sin(a)cos(a)(2cos^2(a) - 1)

Expanding further:

4sin(a)cos(a)(2cos^2(a) - 1) = 8sin(a)cos^3(a) - 4sin(a)cos(a)

And that's the simplified form of the expression 4sin(a)cos(a)(cos^2(a)-sin^2(a)).