Question

If sin2 x - 2sinx = 2, then sinx = _____.

Answer 1

Answer:

$Sin (x) =\frac { 1} { Cos (x) - 1}$

Step-by-step explanation:

Here, given :

sin 2 x - 2 sin x = 2  ....  (1)

Now, by TRIGONOMETRIC IDENTITY:

Sin 2Ф  =  2 SinФ CosФ

⇒  sin 2 x  = 2 sin x cos x

Putting back the value in (1), we get:

sin 2 x - 2 sin x = 2    ⇒  (2 sin x cos x) - 2 sin x = 2

or, 2( sin x  cos x - sin x)  = 2

or, sin x  cos x - sin x  = 1

or, (sin x) ( cosx  - 1)  = 1

⇒ Sin x  = 1 / ( Cos x  - 1)

Hence, $Sin (x) =\frac { 1} { Cos (x) - 1}$

Answer 2

Answer:

sinx = -1

Step-by-step explanation:

This question is from trigonometry.

Given ,

sin2x - 2sinx = 2                             ----------(1)

But sin2x = $2sinx \times cosx$         ----------(2)

Substituting (2) in (1)

$2sinx \times cosx$ -2sinx = 2

2sinx(cosx - 1) = 2

Dividing LHS and RHS by 2 ,

sinx(cosx-1) = 1           ------------(3)

-1  ≤ sinx , cosx ≤ 1

(3) is possible only when

sinx = -1 and cosx = 0

This happens when sinx =270°