If (1+sinx)/cosx=2 then cotx=?

Answer 1

2 = (1+sinx)/cosx
= (sin(x/2) + cos(x/2))^2 / (cos^2(x/2) - sin^2 (x/2))
= (1+tanz)/(1-tanz) ; write x/2 for z
=> tanz = 1/3
now tanx = (2tanz)/(1-tan^z)
= (2/3)/(1-1/9)
= 3/4
=> cotx = 4/3
No more homeworks please...

Answer 2

Square both sides. So
(1+sinx)^2=4(cosx)^2 = 4(1-(sinx)^2)
(sinx)^2 + 2sinx +1 = 4 - 4(sinx)^2
5(sinx)^2 + 2sinx - 3 = 0
Quadratic in sinx gives Sinx = -1, or sinx=3/5, one of which is incorrect because the squaring operation gives a false second root.
If Sinx = -1, then (1+sinx)/cosx = 0, NOT 2 as above.
So sinx=3/5

From the equation; cosx = (1+sinx)/2
So cosx=4/5

cotx = cosx/sinx = 4/3

Answer 3

(1+sinx)/cosx = 2
1+sinx = 2cosx
(1+sinx)² = (2cosx)²
1 + 2sinx + sin²x = 4cos²x = 4 - 4sin²x
5sin²x + 2sinx - 3 = 0
(5sinx - 3)(sinx + 1) = 0
sinx = 3/5, -1
But the solution -1 must be rejected because cosx cannot equal zero.

sin x = 3/5
cos x = √(1 - sin² x) = √(1 - 9/25) = √(16/25) = 4/5

cot x = cos x / sin x = (4/5) / (3/5) = 4/3

Answer 4

1+sinX = 2cosX
(note that cosX can't be 0)

sinX = 2cosX - 1

(sinX)^2 = 4(cosX)^2 - 4cosX + 1

but you know that (sinX)^2 = 1 - (cosX)^2 (formula)

so 1 - (cosX)^2 = 4(cosX)^2 - 4cosX + 1

5(cosX)^2 - 4cosX = 0

and as cosX is not 0:
5cosX = 4

solution:
cosX = 4/5
sinX = 3/5

Answer 5

(1+sinx)/cosx=2
secx+tanx=2
secx=2-tanx

Power the two sides of the equation

(secx)^2=4-4tanx+(tanx)^2

as the formula, (secx)^2=1+(tanx)^2

so,
1+(tanx)^2=4-4tanx+(tanx)^2
4tanx=3
tanx=3/4

so, cotx=1/tanx=4/3

Answer 6

you need to bear with the typing
(1+sin x)/cos x=2
(sin x/2 * sin x/2 +cos x/2*cos x/2 +2 sin x/2 cos x/2) divided by
(cos x/2*cos x/2- sin x/2*sin x/2) =2 --------------------1
using identities 1= sin sqr x+ cos sqr x
sin 2x= 2sinx cosx
cos2x=cos sqr x/2-sin sqr x/2

(sin x/2+ cos x/2)*(sin x/2+cos x/2)/
(cos x/2-sin x/2)(cos x/2+sinx/2) =2

(cos x/2+sin x/2)/(cos x/2-sin x/2)=2-----------------------2

divide numerator and denominator by cos x/2

eqn 2 becomes
(1+tan x/2)/(1-tan x/2)=2

1+tan x/2=2(1-tan x/2)
1+tan x/2=2-2tan x/2
rearranging terms
3tan x/2=1
tan x/2=1/3
x/2 = arctan 1/3
x/2 = (18.43) degree [convert into radian if you wish to]
x=2(18.43)
x=36.86
cot x=cot36.86=4/3=1.33333333

Hope you get good marks if you are submitting an assignment

Answer 7

2/(1+sinx)