What is 2cos^3(pix)+cos^2(pix)-1 ?

The solution to 2cos^3(pix)+cos^2(pix)-1 is 2cos^3(pix)-sin^2(pix)

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simplify 2cos^3(pix)+cos^2(pix)-1

simplify

2 cos^{3} (π x) + cos^{2} (π x) - 1

2 cos^{3} (π x) - sin^{2} (π x)

Solution steps

2 cos^{3} (π x) + cos^{2} (π x) - 1

Use the Pythagorean identity:

1 = cos^{2} (x) + sin^{2} (x)

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

= 2 cos^{3} (π x) - sin^{2} (π x)

tan (x + π) cos (x - \frac{π}{2})

- 3 cos (3 x + π)

(tan (x^{3} + \frac{π}{4}))^{2}

sin (aπ + \frac{π}{3})

sin (\frac{π}{6} + x)

What is 2cos^3(pix)+cos^2(pix)-1 ?
The solution to 2cos^3(pix)+cos^2(pix)-1 is 2cos^3(pix)-sin^2(pix)