Cos 68 - cos 22 / sin 68 - sin 22

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вопрос

To simplify this expression, we need to use the trigonometric identity:

cos (A - B) = cos A cos B + sin A sin B

Using this identity, we can rewrite the expression as:

cos 68 - cos 22 / sin 68 - sin 22
= (cos 68 cos 22 + sin 68 sin 22) / (sin 68 - sin 22)

= (cos (68 - 22)) / (sin 68 - sin 22)

= (cos 46) / (sin 68 - sin 22)

Since cos 46 is a constant value, we can further simplify the expression by finding the values of sin 68 and sin 22:

sin 68 = sin (90 - 22) = cos 22 = 0.927
sin 22 = sin 22 = 0.374

Now we can substitute these values back into the expression:

= cos 46 / (0.927 - 0.374)

= cos 46 / 0.553

= 0.718 / 0.553

= 1.301

Therefore, the value of cos 68 - cos 22 / sin 68 - sin 22 is approximately 1.301.