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

Question

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

in progress 0
Everleigh 1 week 2021-09-12T06:56:13+00:00 2 Answers 0

Answers ( )

    0
    2021-09-12T06:57:29+00:00

    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}

    0
    2021-09-12T06:57:30+00:00

    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°

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )