Cos^2x\3- sin ^2x/3=1

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To solve this equation, we can first simplify it by using the Pythagorean identity for cosine and sine functions:

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

Now, we can substitute this into the original equation:

cos^2(x)/3 - sin^2(x)/3 = 1

Then, we can multiply the entire equation by 3 to get rid of the fractions:

cos^2(x) - sin^2(x) = 3

Now, we can substitute the Pythagorean identity again:

1 - sin^2(x) - sin^2(x) = 3

1 - 2sin^2(x) = 3

-2sin^2(x) = 2

sin^2(x) = -1

Since the square of a real number cannot be negative, there are no solutions to this equation.