Cos 64°×cos19°+sin19°×sin 64°

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вопрос

To find the value of cos(64°) × cos(19°) + sin(19°) × sin(64°), we can use the trigonometric identity for the cosine of the sum of two angles:

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

Plugging in the values of a = 64° and b = 19°:

cos(64° + 19°) = cos(64°) × cos(19°) - sin(64°) × sin(19°)

cos(83°) = cos(64°) × cos(19°) - sin(64°) × sin(19°)

Now, sin(83°) = cos(180° - 83°) = cos(97°)

Since cos(83°) and cos(97°) are cofunctions, they are equal. Therefore,

cos(83°) = cos(64°) × cos(19°) - sin(64°) × sin(19°) = cos(97°)

Therefore, cos(64°) × cos(19°) - sin(64°) × sin(19°) = cos(97°)
cos(64°) × cos(19°) + sin(19°) × sin(64°) = cos(97°)

Thus, the value of the expression is cos(97°).