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

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

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cos(2x)sin(x)=1

cos (2 x) sin (x) = 1

x = \frac{3 π}{2} + 2 πn

Solution steps

cos (2 x) sin (x) = 1

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

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

No Solution

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

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

sin (θ) = 10

17. 6^{2} = 1 5^{2} + 13. 1^{2} - 2 (15) (13.1) \cdot cos (A)

x, f = cos (\frac{1}{x ^{2}})

sin (θ) = 45

cot (θ) + 2 csc (θ) = 6

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