Question

Sin80 --------- 2cos40

Answer 1

Sin 80° = sin (90° - 10°) = cos 10°

2 cos 40° = 2 cos (90° - 50°) = 2 sin 50°

Answer 2

To simplify the expression, let's use the trigonometric identity:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Using this identity, we can rewrite the expression as:

sin(80°) / (2cos(40°))

Now, let's substitute the values:

sin(80°) ≈ 0.9848 cos(40°) ≈ 0.7660

Plugging in these values, we have:

0.9848 / (2 * 0.7660)

Performing the multiplication:

0.9848 / 1.532

Evaluating the division:

≈ 0.6424

Therefore, sin(80°) / (2cos(40°)) is approximately equal to 0.6424.