Given TaNx = 2, tany = 3, x, y ∈ (0, π / 2), find x + y

Given TaNx = 2, tany = 3, x, y ∈ (0, π / 2), find x + y

tan(x+y)
=(tanx+tany)/(1-tanxtany)
=-1
x+y=3π/4

SiNx + cosx > 0, then x is the angle of the first quadrant
If SiNx + cosx is greater than 1, then x must be an acute angle proposition
0 - resolution time: 2009-11-29 19:19
Questioner: 421200339 - first level best answer false proposition
Take a counter example
For example, x = 405 degrees
Then sin405 + cos405 = sin45 + cos45 = √ 2 > 1
Obviously 405 degrees is not an acute angle
So the correct way to say it is, SiNx + cosx > 0, then x is the angle of the first quadrant

False proposition
SiNx + cosx = sin (x + 45) twice the root sign
If SiNx + cosx > 1, then x is the first quadrant angle

Given TaNx = 3, then tan2 (x - π / 4) is equal to

Tan2 (x - Π / 4) = {2tan (x - Π / 4)} / {1-tan2 (x - Π / 4)}, so tan2 (x - Π / 4) = {TaNx Tan Π / 4} / {1 + TaNx * Tan Π / 4} = (3-1) / (1 + 3 * 1) = 1 / 2, so tan2 (x - Π / 4) = (2 * 1 / 2) / (1 - (1 / 2) 2) = 4 / 3

Limx tends to 0 (1-cos2 / x) x / (TaNx SiNx)

Limx tends to 0 (1-cos2 / x) x / (TaNx SiNx)
=Limx tends to 0 (1-cos2 / x) x / TaNx (1-cosx)
=Limx tends to 0 [(x / 2) & # 178; X / 2] / X (X & # 178 / 2)
=1 / 4 (1 / 4)

How about cosx SiNx / cos + SiNx equal to 1-tanx / 1 + TaNx!

One cos x is extracted from the numerator denominator and is reduced to 1-tanx / 1 + TaNx

Cos X / 1-sinx = TaNx / 2, please help me find out how to get the next step. Thank you

Left = {[cos (x / 2)] ^ 2 - [sin (x / 2)] ^ 2} / [cos (x / 2) - sin (x / 2)] ^ 2
=【cos（x/2)+sin（x/2)】/ 【 cos（x/2）- sin（x/2）】
=【1+tanx/2】/【1-tanx/2】
=tan（π/4+x/2)
Right = TaNx / 2
Left and right
Come again when you get the topic right

The root of equation x where the square minus BX plus 22 equals 0 is 5 minus the root sign 3. Find B and the other root

Take the first root in first
(5-radical 3) ^ 2-B (5-radical 3) + 22 = 0
B = 10
So, the original equation: x ^ 2-10x + 22 = 0
Weida theorem X1 + x2 = - B / A
So, (5-root 3) + the other root = 10
The other one = 5 + 3

Given that the root 2 is a root of the equation x with respect to x, where the square of x minus x plus a equals 0, find the square of a minus 2 minus a plus 2 / 2 A

Is the question wrong

Given the circle O: x ^ 2 + y ^ 2 = 9 and passing through the fixed point P (1,2) as two mutually perpendicular chords, AB and CD, then the trajectory equation of the midpoint m of the line AC is obtained

Let two points on a circle be a (a, b), C (C, d), m (x, y): A & # 178; + B & # 178; = 9 (1) C & # 178; + D & # 178; = 9 (2) x = (a + C) / 2, a + C = 2x (3) y = (B + D) / 2, B + D = 2Y (4) AP & # 178; + CP & # 178; = AC & # 178; (a - 1) &# 178; + (B - 2) &# 178; +

From the secant ABC of a (4,0) leading circle x 2 + y 2 = 4, the trajectory equation of midpoint P of chord BC is obtained

Method 1: let P (x, y) be connected with OP, then op ⊥ BC (2) when x ≠ 0, Kop · KAP = - 1, that is, YX · YX − 4 = - 1, that is, X2 + y2-4x = 0 (8) when x = 0, the coordinates of point P (0, 0) are the solution of the equation (★) (12 points) BC point P of