Question

4 sin 16 cos16 /sin32​

Answer 1

$\frac{4sin(16)cos(16)}{sin(32)}=\frac{2sin(32)}{sin(32)}=2$

Answer 2

To simplify the expression 4 sin(16°) cos(16°) / sin(32°), we can use trigonometric identities. Specifically, we can use the double-angle identity for sine and the identity for the product of two sines.

The double-angle identity for sine is: sin(2θ) = 2sin(θ)cos(θ)

Now, let's use this identity to rewrite the expression:

4 sin(16°) cos(16°) / sin(32°)

= 2 * 2 sin(16°) cos(16°) / sin(32°)

= 2 * sin(32°) / sin(32°) (using the double-angle identity sin(2θ) = 2sin(θ)cos(θ))

= 2

Therefore, the simplified expression is 2.