Tana + COTA = 3, a is an acute angle, Tan ^ A + cot ^ a =?

Tana + COTA = 3, a is an acute angle, Tan ^ A + cot ^ a =?

Acute angle, Tana > 0
(tanA+1/tanA)^2=3*3=9
tan^A+1/tan^A+2=9
tan^A+cot^A=tan^A+1/tan^A=7

If Tana + COTA = 3 and a is an acute angle, then tan? A + cot? A =?

（tana+cota）^2=9 tan2a+cot2a+2=9 tan2a+cot2a=7

If Tana + COTA = 9 / 4, then the value of Tan ^ 2A + secacsca + cot ^ 2 is given

tana+cota=(sin²a+cos²a)/(sinacosa)=1/(sinacosa)=secacsca=9/4
tan²a+secacsca+cot²a
=(tana+cota)²-2+secacsca
=81/16-2+9/4
=85/16

Let Tana + COTA = 4. Find the value of sinacosa

sinα／cosα＋cosα／sinα＝4
﹙sin²α＋cos²α﹚／sinα cosα＝4
1／sinα cosα＝4
sinα cosα＝1/4

Tan (α + π) is known 4)＝1 3． (I) find the value of Tan α; (II) find 2sin2 α - sin (π - α) sin (π) 2−α)+sin2(3π 2 + α)

（Ⅰ）∵tan(α+π
4)＝tanα+1
1−tanα＝1
3，∴tanα＝−1
2．
(II) original formula = 2sin2 α - sin α cos α + Cos2 α
=2sin2α−sinαcosα+cos2α
sin2α+cos2α=2tan2α−tanα+1
tan2α+1=2×(−1
2)2−(−1
2)+1
(−1
2)2+1＝8
5．

Given Tana COTA = 1, find the value of tan3 square a-cot3 square a

（tana-cota）²=1
tan²a+cot²a-2=1
tan²a+cot²a=3
tan³a-cot³a
=（tana-cota)(tan²a+cot²a+2)
=1×(3+2)
=5

Tana + COTA = 3, (a acute angle) find the square of Tana + COTA?

tanA+cotA=3
Square on both sides
Square of Tana + square of COTA + 2tana * COTA = 9
Tana * COTA = 1
So the square of Tana + the square of COTA = 7

It is known that 3 / 4 is less than a and less than W, and Tana + COTA is equal to - 10 / 3,

If Tana = x, then x 2 + 1 / x = - 10 / 3, x = - 3 or x = - 1 / 3 can be obtained. According to the range of X, x = - 1 / 3, so a = arctan (- 1 / 3), about 162 degrees

Given that log (Tana + COTA) is the base, Sina = - 3 / 4, and a belongs to (0,2 / π), log Tana is the value of bottom cosa

tana+cota=sina/cosa+cosa/sina=(sin²a+cos²a)/sinacosa=1/sinacosalgsina/lg(1/sinacosa)=-3/4lgsina/lg(sinacosa)=3/4lgsina/(lgsina+lgcosa)=3/4(lgsina+lgcosa)/lgsina=4/31+lgcosa/lgsina=4/3lgcosa/...

Why is the base number in log [Tana] cosa = > log [Sina] cosa / (1-log [Sina] COSA) [ Why log [Tana] cosa can deduce = > log [Sina] cosa / (1-log [Sina] COSA)

log[tana]cosa
=log[tana](sina/tana)
=log[tana]sina-1
=1/log[sina]tana-1
=1/log[sina](sina/cosa)-1
=1/(1-log[sina]cos)-1
=log[sina]cosa/(1-log[sina]cosa)