What is the general solution for 3sin(x)-cos(2x)=1 ?

The general solution for 3sin(x)-cos(2x)=1 is x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Subtract

1

from both sides

3 sin (x) - cos (2 x) - 1 = 0

Rewrite using trig identities

- 2 + 2 sin^{2} (x) + 3 sin (x) = 0

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 2 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

20 = 15 cos (x) \cdot 2, 47

\frac{[ sin ( x ) + cos ( x ) ]}{cos ( x )} = sin (x) + 1

cos (A) = 0.4639

csc (A) = \frac{9.43}{5}

cos (x) cos (3 5^{\circ}) = 1 - sin (x) sin (3 5^{\circ})

What is the general solution for 3sin(x)-cos(2x)=1 ?
The general solution for 3sin(x)-cos(2x)=1 is x= pi/6+2pin,x=(5pi)/6+2pin