Tan (a + b) = 2 / 5, Tan (a + π / 4) = 3 / 22, then Tan (B - π / 4) is equal to?

Tan (a + b) = 2 / 5, Tan (a + π / 4) = 3 / 22, then Tan (B - π / 4) is equal to?

Let x = Tan (B - π / 4)
y=tan(a+π/4)=3/22
tan(a+b)=tan[(a+π/4)+(b-π/4)]=2/5
So (x + y) / (1-xy) = 2 / 5
2-3x/11=5x+15/22
tan(b-π/4)=x=4

Given that Tan (α + β) = 25, Tan (α + π 4) = 322, then Tan (β − π 4) is equal to ()
A. 15B. 14C. 1318D. 1322

Because Tan (α + β) = - 1, Tan (α + π 4) = 322 ﹣ Tan (β − π 4) = Tan [(α + β) - (α + π 4)] = Tan (α + β) − Tan (α + π 4) 1 + Tan (α + β) Tan (α + π 4) = 25 − 3221 + 25 × 322 = 14, B is selected

Given sin (30 ° + α) = 35, 60 ° < α < 150 °, the value of cos α is 0______ ．

Given sin (30 ° + α) = 35, 60 ° < α < 150 °, the value of cos α is 0______ ．

Let f (a) = 2sina cos a + cos A / 1 + Sin & # 178; a + cos (3 π / 2 + a) - Sin & # 178; (π / 2 + a) (1 + 2sina ≠ 0)
Find the value of f1f2f3.f89

=(2sinacosa+cosa)/(1+sin^2a+sina-cos^2a)
=cosa(1+2sina)/sina(1+2sina)=cosa/sina=cota
If a is a degree
It's very simple: cot1 ° * cot89 ° = 1, cot2 ° * cot88 ° = 1
f1f2f3.f89=cot45=1

If a is an obtuse angle, find sin ^ 3A cos ^ 3A / 2sina cosa
Is sin to the third power a-cos to the third power a divided by 2sina cosa

What do you mean, write it clearly!

Simple application of acute angle trigonometric function (2)
16 (Ningbo) according to the forecast of the meteorological station, the center of a strong typhoon is located on the sea surface of the southeast direction (366 + 1082) km of Ningbo (urban area, the same below). At present, the center of the typhoon is moving 60 ° north by west at the speed of 20 km / h, and the circular area 50 km away from the center of the typhoon will be strongly attacked, Xiangshan is located 56 kilometers to the north by east of Ninghai. May I ask if Ningbo, Ninghai and Xiangshan will be hit by the typhoon? If so, ask for the time of the strong attack; if not, please explain the reason. (in order to solve the problem, we need to draw a schematic diagram, some of which have been drawn, please complete the diagram as needed.)

The East-West (horizontal) straight line intersects with the (north-south) extension line to extend the moving rays of the typhoon center, and intersects with ∵, 45 °, ∵, ∵ 30 °, ∵ 30 ° =, ∵ and coincides with ∵. The typhoon center must pass through Ninghai. The time of passing through Ninghai is (hour)

In RT triangle ABC, angle c = RT, angle AC = 5, BC = 7
Find the sine cosine and tangent of angle A and angle B

First, we use Pythagorean theorem to calculate the long root number 17 of ab. the positive value of angle a is the root number 17 of BC compared with ab = 7 times compared with ab = 17, and the cosine of angle a is the root number 17 of AC compared with ab = 5 times compared with ab = 17
Let the tangent of a be BC to AC = 7:5 = 7 / 5
Angle B uses the same method, SINB = 7 root 17 / 17, CoSb = 5 root 17 / 17, tanb = 7 / 5

Acute trigonometric function of a simple problem!
2 cos 30 ° - Tan 60 ° =? 2. √ 2-1 / 1-3 Tan & sup2; 30 ° + 2 √ (sin 45 ° - 1) & sup2;
Just answer the first one. I'll give you more points for the second one.

1.2cos30°-tan60°=√3-√3=0
2.1-3tan²30°+2√（sin45°-1）²
=1-3*(√3/3)²+2*(1-√2/2)
=2-√2

RT △ ABC, ∠ C is right angle
Knowing the length of three sides, how to find the slope of the hypotenuse?

Slope of hypotenuse = tangent of slope angle = opposite side: adjacent side