What is the general solution for ((2sin(x))(sin(x)))/(sin(x))+1=3 ?

The general solution for ((2sin(x))(sin(x)))/(sin(x))+1=3 is x= pi/2+2pin

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((2sin(x))(sin(x)))/(sin(x))+1=3

\frac{( 2 sin ( x ) ) ( sin ( x ) )}{sin ( x )} + 1 = 3

x = \frac{π}{2} + 2 πn

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{( 2 sin ( x ) ) ( sin ( x ) )}{sin ( x )} + 1 = 3

Simplify

\frac{2 sin ( x ) sin ( x )}{sin ( x )} + 1 : 2 sin (x) + 1

\frac{2 sin ( x ) sin ( x )}{sin ( x )} + 1

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

\frac{2 sin ( x ) sin ( x )}{sin ( x )}

2 sin (x) sin (x) = 2 sin^{2} (x)

2 sin (x) sin (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= 2 sin^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= 2 sin^{2} (x)

= \frac{2 sin ^{2} ( x )}{sin ( x )}

Cancel the common factor:

sin (x)

= 2 sin (x)

= 2 sin (x) + 1

2 sin (x) + 1 = 3

Move

1

to the right side

2 sin (x) + 1 = 3

Subtract

1

from both sides

2 sin (x) + 1 - 1 = 3 - 1

Simplify

2 sin (x) = 2

2 sin (x) = 2

Divide both sides by

2

2 sin (x) = 2

Divide both sides by

2

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

Simplify

sin (x) = 1

sin (x) = 1

General solutions for

sin (x) = 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

tan (2 θ) = - \frac{2}{5}

cos (2 x) - 3 cos (x) = - 2

3 cos (x) - 3 sin (x) = 0

cos^{2} (3 x) = cos (9 x^{2})

2 cos (θ) - 2 = 0

What is the general solution for ((2sin(x))(sin(x)))/(sin(x))+1=3 ?
The general solution for ((2sin(x))(sin(x)))/(sin(x))+1=3 is x= pi/2+2pin