How is cos = - radical 2 / 2 equal to 135?

How is cos = - radical 2 / 2 equal to 135?

There is a theorem that the cosine of an angle is equal to the opposite number of the complementary angle cosine, because the cosine of 45 ° is the root of 2 / 2, and its complement angle is 135 ° so it is - 2 / root 2. In addition, the sine of an angle is equal to the sine of its complement angle, and the tangent of an angle is equal to the opposite number of its complement tangent,

How much is cos 660 degree equal to? What is sin square 120 degree equal to under root sign?

cos660=cos(660-720)=cos(-60)=cos60=0.5
Sin120 = sin60 = root 3 divided by 2
In the question, the square of sin under the root sign is 120 degrees. The answer in this question is the same, that is, the root sign 3 divided by 2

When α is an obtuse angle, the value of sin α / Radix 1-cos square α + cos α / Radix 1-sin square α is

solution
1-cos²α=sin²α
1-sin²α=cos²α
Alpha is an obtuse angle,
So sin α > 0, cos α < 0
So the original formula = sin α / | sin α| + cos α / | cos α|
=sinα/sinα+cosα/(-cosα)
=1-1
=0

Comparison size: root 13 root 11 and root 15 root 13 Want details!

Compare their reciprocal, because they are all positive, but the larger the reciprocal is, the smaller
The reciprocal of root 13-root 11 should be rational, which is equal to (root 13 + root 11) / (root 13-root 11) (root 13 + root 11) = (root 13 + root 11) / 2
Similarly, root 15 root 13 = (root 15 + root 13) / 2
Obviously, the back is larger than the front. On the contrary, root 13 root 11 > root 15 root 13

Compare the difference between root 15 minus root 14 and root 14 minus root 13

A = (√ 15 - √ 14) B = (√ 14 - √ 13) a / b = (√ 15 - √ 14) / (√ 14 - √ 13) up and down times (√ 14 + √ 13) (√ 14 + √ 15), a / b = (√ 15 - √ 14) (√ 14 + √ 13) (√ 14 + √ 15) / [(√ 14 - √ 13) (√ 14 + √ 15)] = (√ 14 + √ 13) / (√ 14 + √ 15)

Compare the size of root number 15 - root 14 and root 14 - root 13

Molecular rational radical 15 - radical 14 = (root 15 - root 14) (root 15 + root 14) / (root 15 + root 14) = (15-14) / (root 15 + root 14) = 1 / (root 15 + root 14) similarly, root 14 - root 13 = 1 / (root 14 + root 13) and root 15 > root 13

The ratio of root number 15 to root 13 to root number 11

(root 15-root 13) * (root 15 + root 13) = 15-13 = 2=
(root 13-root 11) * (root 13 + root 11) = 13-11 = 2
because:
Root 13 + root 15 > root 13 + root 11
Then radical 15 - radical 13

Root 15 minus root 13 and root 13 minus root 11 Compared with the size and process

Because (√ 15 - √ 13) * (√ 15 + √ 13) = (√ 15) ^ 2 - (√ 13) ^ 2 = 15-13 = 2 (√ 13 - √ 11) * (√ 13 + √ 11) = (√ 13) ^ 2 - (√ 11) ^ 2 = 13-11 = 2, (√ 15 - √ 13) = (√ 13 - √ 11) * (√ 13 + √ 11) and (√ 15 - √ 13) > (√ 13 + √ 11) (√ 15 - √ 13)

Comparison size: the difference between radical 15-13 and 13-11

The reciprocal of Radix 15 to Radix 13 is 1 / 2 (Radix 15 + Radix 13)
The reciprocal of root 13 and root 11 is 1 / 2 (root 13 + root 11)
So root 15 - radical 13

Compare the size of root 7-6 and root 6-5 Please be more specific and don't assume

The reciprocal of √ 7 - √ 6 is √ 7 + √ 6
The reciprocal of √ 6 - √ 5 is √ 6 + √ 5
∵√7+√6＞√6+√5
∴√7-√6＜√6-√5