Question

cos26cos14 - cos64cos76-cos40упростите выражениепомооогите пожалуста, срочно

Answer 1

Заменяешь cos 64 на sin 26, а cos 76 на sin 14

 

Получается: cos26cos14-sin26sin14 - cos 40 = cos (26+14) - cos 40 = cos 40 - cos 40 = 0

 

cos26cos14-sin26sin14 - это формула сложения косинусов - cos (альфа + бета)

Answer 2

Simplifying Trigonometric Expression

To simplify the given expression cos(26)cos(14) - cos(64)cos(76) - cos(40), we can use the trigonometric identity:

cos(A)cos(B) = 0.5[cos(A+B) + cos(A-B)]

Applying this identity to the given expression, we get:

0.5[cos(26+14) + cos(26-14)] - 0.5[cos(64+76) + cos(64-76)] - cos(40)

Simplifying further:

0.5[cos(40) + cos(12)] - 0.5[cos(140) + cos(-12)] - cos(40)

Now, we can use the fact that cos(-x) = cos(x):

0.5[cos(40) + cos(12)] - 0.5[cos(140) + cos(12)] - cos(40)

Final Simplified Expression

Combining like terms, the final simplified expression is:

0.5[cos(40) - cos(140)] - cos(40)

This is the simplified form of the given trigonometric expression.