sin4x-cos2x=0 How do you solve?
How do you solve the equation sin(4x) - cos(2x) = 0? I would appreciate a step-by-step explanation of the solution process, including any relevant identities or methods that can be used to find the values of x. Thank you!
3 Answers
sin(4x) - cos(2x) = 0
2sin(2x)cos(2x) - cos(2x) = 0
cos(2x)(2sin(2x) - 1) = 0
cos(2x) = 0
in which case
2x = pi/2, 3pi/2, 5pi/2
x = pi/4, 3pi/4, 5pi/4
x = (pi/4 + npi/2) where n is an integer
or
2sin(2x) - 1 = 0
2sin(2x) = 1
sin(2x) = 1/2
2x = pi/6, 5pi/6, 13pi/6, 17pi/6, ...
x = pi/12, 5pi/12, 13pi/12, 17pi/12, ...
sin4x + cos2x = 0 2sin2x . cos2x + cos2x =0 cos 2x ( 2sin 2x +a million) =0 cos 2x =0 2x=nkp + p/2 x =nkp/2 + p/4 2sin 2x +a million =0 sin2x =-a million/2 2x =2kp -p/6 x=kp- p/12 2x =2kp +7p/6 x=kp + 7p/12
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