Verify whether the statement is true.

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SUMMARY

The equation 2cos²(4x) - 1 = 0 is solved by substituting x = π/16 and x = 3π/16. The transformation involves letting u = cos(x) and v = 4x, leading to the equation 2u² - 1 = 0. The solution requires evaluating cos(π/4), which equals √2/2, and squaring it to confirm the equation holds true. The key solutions derived from this equation are x = π/16 and x = 3π/16.

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Homework Statement


2cos^2 4x-1=0

a)x= pi/16 x=3pi/16


Homework Equations





The Attempt at a Solution


a) x=pi/16

u=cosx
v=4x
2u^2 v-1=0
i'm stuck here
 
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are you solving this equation: 2 * cos^2(4x) - 1 = 0

first plugin the x=pi/16 --> 4x = pi/4 and so you have 2 * cos^2(pi/4) - 1 = 0

so what is cos(pi/4)? then square it and solve.
 
maxtheminawes said:

Homework Statement


2cos^2 4x-1=0
What does this mean? I can think of at least two interpretations. Use parentheses to make the meaning clear.
maxtheminawes said:
a)x= pi/16 x=3pi/16


Homework Equations





The Attempt at a Solution


a) x=pi/16

u=cosx
v=4x
2u^2 v-1=0
i'm stuck here
 

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