find the xact value 4:?

Question

2sin x tan x - tan x= 1-2sin x

Answer 1

tan x (2sin x - 1) = - (2 sin x - 1)
tan x (2sin x - 1) + (2sin x - 1) = 0
(2 sin x - 1)(tan x + 1) = 0
sin x = 1 / 2 , tan x = - 1
x = 30 ° , 150° , 135° , 315°
or
x = π / 6 , 5π / 6 , 3π / 4 , 7π / 4

Answer 2

2sinxtanx - tanx = 1 - 2sinx
tanx (2sinx - 1) = -2sinx + 1
tanx (2sinx - 1) = -(2sinx - 1) << Equation 1

From here, we have 2 cases.


Case 1
> 2sinx - 1 = 0 << Equation 2
If 2sinx - 1 = 0, then we cannot divide Equation 1 by 2sinx - 1, as doing so would mean dividing by 0, which would give an undefined answer. It is a common mistake of many to divide immediately by a common factor without taking into consideration the possibility of it being 0.

Instead, we can find the value of x from Equation 2.

2sinx - 1 = 0
2sinx = 1
sinx = 1/2

There are 2 values of x for which sinx = 1/2, namely, 30 and 150.



Case 2
> 2sinx - 1 is not equal to 0

Accordingly, we can divide Equation 1 by 2sinx - 1 since it is not equal to 0.

[tanx (2sinx - 1) = -(2sinx - 1)] / (2sinx - 1)
tanx = -1
x = 135 and 315

Thus, the possible values of x are 30, 150, 135 and 315

Answer 3

2sin x tan x - tan x= 1-2sin x

tan x (2 sin x - 1) = 1- 2 sin x
- tan x (1- 2 sinx ) = 1- 2 sinx
-tan x = 1
tan x = -1

x = -45 or 135 or these values + multiples of 360

Answer 4

2sin x tan x - tan x= 1-2sin x

=> tanx (2sinx-1) =1-2sinx
( - 1) tanx (1-2sinx) = 1-2sinx
tanx =-1
x = -45 degrees or 360 -45 =315 degrees

Answer 5

To solve trig equations, start by putting all the parts in terms of sin and cos.

It looks like common denominators would help with this problem

2 sinx * sinx sinx
----------------- - ----------- = 1 - 2sinx
cosx cosx

2 sin^2(x) - sinx = cosx (1 - 2sinx)
sinx (2 sinx - 1) = cosx (-1) (2sinx - cosx)
sinx/cosx = -1
tanx = -1

... okay, now I need a calculator ... but this should give you the answer.

Remember: the same rules apply to sinx and cosx as to x and y when you are solving them.

If it makes it easier, redefine your problem as follows:
sinx = a
conx = b
tanx = sinx/cosx = a/b

so your question is really:
2a * a/b - a/b = 1 - 2a

(simplify as I did above)

a/b = -1

Have fun and keep practicing. Just write out all your steps and be careful with your algebra rules

Answer 6

2sin x tan x - tan x= 1-2sin x

=> 2sin x tan x - tan x - 1 + 2sin x = 0
=> 2sin x (tan x + 1) - 1(tan x + 1) = 0
=> (2sin x - 1) (tanx + 1) = 0
=> sin x = 1/2 or tan x = - 1
=> sin x = sin (π/6) or tan x = tan ( -π/4)
=> x = kπ + (-1)^k (π/6) or x = kπ - π/4, k ∈ Z.

Answer 7

2sinxtanx -- tanx = 1 -- 2sinx
Or (2sinx -- 1)(tanx + 1) = 0
giving sinx = 1/2 = sin 30 deg hence x = 30 deg, 150deg,
and tanx = -- 1 = tan 135 deg, hence x = 135 deg, 225 deg,

Answer 8

tanx = -1
x is 135 or 315 degrees ( +360 as many times)