Question

Докажите тождество:

Answer 1

Посмотрим на знаменатель: tgα + ctgα = Sinα/Cosα + Cosα/Sinα =
=(Sin²α + Cos²α)/SinαCosα= 1/(SinαCosα)
вот теперь разделим 1 на эту дробь и получим: SinαCosα

Answer 2

Proof of the Identity: 8sin10*sin50*sin70=130

To prove the identity 8sin10*sin50*sin70=130, we can use the trigonometric identities and properties of sine and cosine functions.

Let's break down the proof step by step:

Step 1: Express the angles in terms of their sine and cosine values. - We know that sin(a) = b/c and cos(a) = a/c, where a, b, and c are the sides of a right triangle. - In this case, we have three angles: 10, 50, and 70 degrees.

Step 2: Express the given identity in terms of sine and cosine. - The given identity is 8sin10*sin50*sin70=130.

Step 3: Substitute the values of sine and cosine. - Using the trigonometric identities, we can substitute the values of sine and cosine for the given angles.

Step 4: Simplify the expression. - After substituting the values, we can simplify the expression to verify if it equals 130.

Unfortunately, the search results did not provide the necessary information to complete the proof of this specific identity. Therefore, we are unable to provide a detailed proof at this time.

If you have any other questions or need further assistance, feel free to ask!