Question

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

Answer 1

sinx = -1

Explanation:

This question is from trigonometry.

Given ,

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

But sin2x =
`2sinx * cosx` ----------(2)

Substituting (2) in (1)

`2sinx * 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°

Answer 2

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

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}`