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

The general solution for sin(3x)cos(2x)+cos(3x)sin(2x)=1 is x= pi/(10)+(2pin)/5

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

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

x = \frac{π}{10} + \frac{2 πn}{5}

Solution steps

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

Rewrite using trig identities

sin (3 x + 2 x) = 1

General solutions for

sin (3 x + 2 x) = 1

3 x + 2 x = \frac{π}{2} + 2 πn

Solve

3 x + 2 x = \frac{π}{2} + 2 πn : x = \frac{π}{10} + \frac{2 πn}{5}

x = \frac{π}{10} + \frac{2 πn}{5}

tan^{2} (θ) + 4 tan (θ) = 3

3 cot (θ) + 7 = 0

sin^{2} (x) - 4 sin (x) = 0

sin^{2} (x) - cos (x) - 1 = 0

3 tan (2 θ) + 1 = 0

What is the general solution for sin(3x)cos(2x)+cos(3x)sin(2x)=1 ?
The general solution for sin(3x)cos(2x)+cos(3x)sin(2x)=1 is x= pi/(10)+(2pin)/5