Question

Cos38 / cos19 -sin 19 - sin19​

Answer 1

ОТВЕТ: Cos(38)/cos(19) - 2sin19

Answer 2

To simplify the expression, let's use trigonometric identities to rewrite the terms. First, recall the double-angle identities:

1. cos(2θ) = cos²(θ) - sin²(θ)
2. sin(2θ) = 2 * sin(θ) * cos(θ)

Now, let's simplify the expression step by step:

cos(38°) = cos(19° + 19°) Using the double-angle identity (1):

cos(38°) = cos²(19°) - sin²(19°)

Next, we'll use the Pythagorean identity:

sin²(θ) + cos²(θ) = 1

So, we can rewrite the expression for cos(38°):

cos(38°) = 1 - sin²(19°)

Now, we'll deal with the sin(19°) terms:

sin(19°) + sin(19°) = 2 * sin(19°)

Now, putting it all together, the simplified expression is:

(cos(38°) / (cos(19°) - sin(19°))) - (2 * sin(19°))

Replacing cos(38°) with the previous expression:

((1 - sin²(19°)) / (cos(19°) - sin(19°))) - (2 * sin(19°))

Now, we need to find a common denominator for the fraction:

((1 - sin²(19°)) - (2 * sin(19°) * (cos(19°) - sin(19°)))) / (cos(19°) - sin(19°))

Now, expand the terms:

(1 - sin²(19°) - 2 * sin(19°) * cos(19°) + 2 * sin²(19°)) / (cos(19°) - sin(19°))

Combine like terms:

(1 + sin²(19°) - 2 * sin(19°) * cos(19°)) / (cos(19°) - sin(19°))

Now, use the Pythagorean identity again:

sin²(θ) + cos²(θ) = 1 => cos²(θ) = 1 - sin²(θ)

Replace cos²(19°) with the identity:

(1 + sin²(19°) - 2 * sin(19°) * cos(19°)) / (cos(19°) - sin(19°))

(1 + sin²(19°) - 2 * sin(19°) * (sqrt(1 - sin²(19°)))) / (cos(19°) - sin(19°))

Now, the expression is in terms of sin(19°). If you have a specific value for sin(19°), you can substitute it in the expression to get the final numerical result.