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The general solution of the equation 2cos2x=3.2cos²x-4 is?

Answer 1

No real solution.

#2cos2x=3.2cos^2 x -4# #2cos2x=16/5cos^2 x-4|-(16/5cos^2 x-4)# #2cos2x-16/5cos^2(x)+4=0|* 5/2# #5cos2x-8cos^2(x)+10=0# #color(blue)(cos(2x)=2cos^2(x)-1)# #5 * (color(blue)(2cos^2(x)-1))-8cos^2(x)+10=0# #2cos^2(x)+5=0# #cos^2(x)=-5/2# #cos(x)=sqrt(-5/2)# There is no real solution since the radicand is negative.

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Answer 2

James Adkins

To find the general solution of the equation (2\cos(2x) = 3.2\cos^2(x) - 4), follow these steps:

Rewrite (2\cos(2x)) using the double angle identity: (2\cos(2x) = 2(2\cos^2(x) - 1)).
Substitute (2(2\cos^2(x) - 1)) for (2\cos(2x)) in the equation: (2(2\cos^2(x) - 1) = 3.2\cos^2(x) - 4).
Simplify the equation.
Solve the resulting quadratic equation for (\cos(x)).
Find the solutions for (x) using the values of (\cos(x)).
Express the solutions in terms of (x), representing the general solution.

The general solution of the equation (2\cos(2x) = 3.2\cos^2(x) - 4) is determined by solving the resulting quadratic equation for (\cos(x)) and finding the corresponding values of (x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.