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Popular >

(m+1)sin(x)+2-m=0

Solution

(m + 1) sin (x) + 2 - m = 0

Solution

x = arcsin (\frac{m - 2}{m + 1}) + 2 πn, x = π + arcsin (- \frac{m - 2}{m + 1}) + 2 πn

Solution steps

(m + 1) sin (x) + 2 - m = 0

Move

m

to the right side

(m + 1) sin (x) + 2 - m = 0

Add

m

to both sides

(m + 1) sin (x) + 2 - m + m = 0 + m

Simplify

(m + 1) sin (x) + 2 = m

(m + 1) sin (x) + 2 = m

Move

2

to the right side

(m + 1) sin (x) + 2 = m

Subtract

2

from both sides

(m + 1) sin (x) + 2 - 2 = m - 2

Simplify

(m + 1) sin (x) = m - 2

(m + 1) sin (x) = m - 2

Divide both sides by

m + 1; m \neq = - 1

(m + 1) sin (x) = m - 2

Divide both sides by

m + 1; m \neq = - 1

\frac{( m + 1 ) sin ( x )}{m + 1} = \frac{m}{m + 1} - \frac{2}{m + 1}; m \neq = - 1

Simplify

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

Simplify

\frac{( m + 1 ) sin ( x )}{m + 1} : sin (x)

\frac{( m + 1 ) sin ( x )}{m + 1}

Cancel the common factor:

m + 1

= sin (x)

Simplify

\frac{m}{m + 1} - \frac{2}{m + 1} : \frac{m - 2}{m + 1}

\frac{m}{m + 1} - \frac{2}{m + 1}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{m - 2}{m + 1}

sin (x) = \frac{m - 2}{m + 1}; m \neq = - 1

sin (x) = \frac{m - 2}{m + 1}; m \neq = - 1

sin (x) = \frac{m - 2}{m + 1}; m \neq = - 1

Apply trig inverse properties

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

General solutions for

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (\frac{m - 2}{m + 1}) + 2 πn, x = π + arcsin (- \frac{m - 2}{m + 1}) + 2 πn

x = arcsin (\frac{m - 2}{m + 1}) + 2 πn, x = π + arcsin (- \frac{m - 2}{m + 1}) + 2 πn

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