What is the general solution for 25sin(2x)-50cos(x)=0 ?

The general solution for 25sin(2x)-50cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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25sin(2x)-50cos(x)=0

25 sin (2 x) - 50 cos (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

25 sin (2 x) - 50 cos (x) = 0

Rewrite using trig identities

- 50 cos (x) + 50 cos (x) sin (x) = 0

Factor

- 50 cos (x) + 50 cos (x) sin (x) : 50 cos (x) (sin (x) - 1)

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

Solving each part separately

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

5 sin (2 x) = 3 cos (2 x)

4 cos (3 x - 20) = 1

0 = 1.9 cos (0.1 t) - 1.25 sin (0.2 t)

sin (\frac{x}{4}) = \frac{3}{2}

cos (θ) = \frac{- 3 + ( - 6 )}{( 9 ) ( 18 )}

What is the general solution for 25sin(2x)-50cos(x)=0 ?
The general solution for 25sin(2x)-50cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin