The square root two cos (a) + the root two sin (a) equals ,

The square root two cos (a) + the root two sin (a) equals ,

Root 2 / 2cosa + root 2 / 2sina
=sin45cosa+cos45sina
=sin(45+a)

Sin a + cos A is equal to the root of two. Find the value of 1 / 2 sin square a + 1 / 2 cos square a

sina+cosa=√2/2
Square the two sides
Sin? A + + 2sinacosa + cos? A = 1 / 2, i.e
2sinacosa=sin2a=-1/2
therefore
（1/sin²a）+（1/cos²a）=（1/sin²acos²a）=4/sin²2a=16

Compare the size of root 12 minus root 11 and root 18 minus root 17

√12－√11=1/[√12＋√11]
√18－√17=1/[√18＋√17]
Because: √ 18 ＋√ 17 > √ 12 ＋√ 11
So 1 / [√ 18 ＋√ 17] √ 18 - √ 17

The size of 15 minus 13 and 13 minus 11 See the topic clearly, look carefully

√15-√13
=（√15-√13)(√15+√13)/(√15+√13)
=(15-13)/(√15+√13)
=2/(√15+√13)
In the same way
√13-√11=2/(√13+√11)
√15+√13>√13+√11>0
SO 2 / (√ 15 + √ 13)

The size of 15 minus 13 and 11 (13 minus 11) Compare the size of √ 15 - √ 13 with the size of 13 - √ 11 contained in a radix

Know:
√15 < 4
√13 > 3
Then √ 15 - √ 13 < 1
And 3

Compare the size of root number 18 root 17 and root 14 root 13

Reciprocal method
1 / (root number 18 - root number 17) = root number 18 + root number 17
1 / (root 14 root 13) = root 14 + root 13
∵ root number 18 + root number 17 > root number 14 + root number 13
ν 1 / (root No. 18-root No. 17) > 1 / (root No. 14-root No. 13)
The root number is 18 to the root number is 17

Comparison size: root 6 + root 14 and root 7 + root 13 (need process)

Square the two, left = 20 + 4 times the root number 21
Right = 20 + 2 times root number 91
So root 7 + root 13

Radical 11 root 10____ Root 14 root 13 compare size

√11-√10=1/(√11+√10)
√14-√13=1/(√14+√13)
Because √ 14 + √ 13 > √ 11 + √ 10
So 1 / (√ 11 + √ 10) > 1 / (√ 14 + √ 13)
That is √ 11 - √ 10 > √ 14 - √ 13

Try to compare the size of "root number 10 - root 14 and root number 11 - root 13"

∵ root 10 < root 11, root 13 < root 14
The root number 10 - root number 11 ﹤ 0, the root number 13 ﹤ the root number 14 ﹤ 0
ν (root 10 root 14) - (root 11 root 13)
=(root 10 root 11) + (root 13 root 14) < 0
﹤ root 10 root 14 ﹤ root 11 root 13

Compare the size of root 12 root 11 and root 11 root 10

√12-√11=1/(√12+√11),
√11-√10=1/(√11+√10),
√12>√10==>√12+√11>√10+√11
==>(1/√12+√11)√12-√11