Answered: "solve the following equation for all values of..."

Albarellak

Answered question

2021-03-08

solve the following equation for all values of x:

\sin^{2} x + \sin x \cos x

SoosteethicU

Skilled2021-03-09Added 102 answers

\sin (x) (\sin (x) + \cos (x))

. If this expression equals zero,

\sin (x) = 0

\sin (x) = - \cos (x)

, so

\tan (x) = - 1 .

Solutions:

\sin (x) = 0 : x = n (π), \tan (x) = - 1 : x = (4 n - 1) \frac{π}{4}

where n is an integer. x is in radians. To convert to degrees put

(π) = 180

: 0, 180, 360, ..., 135, 315, ... for example.

\cos (2 x) = 1 - 2 \sin^{2} (x)

, so

\sin^{2} (x) = \frac{1 - \cos (2 x)}{2}

\sin (2 x) = 2 \sin (x) \cos (x)

, so

\sin (x) \cos (x) = (\frac{1}{2}) \sin (2 x)

\sin^{2} (x) + \sin (x) \cos (x) = (\frac{1}{2}) (1 - \cos (2 x) + \sin (2 x))

. Above solutions apply.

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