What is (sin^2(t)-cos^2(t))dt ?

The solution to (sin^2(t)-cos^2(t))dt is -cos(2t)dt

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simplify (sin^2(t)-cos^2(t))dt

simplify

(sin^{2} (t) - cos^{2} (t)) d t

- cos (2 t) d t

Solution steps

(sin^{2} (t) - cos^{2} (t)) d t

Use the Double Angle identity:

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

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

= d t (- cos (2 t))

Remove parentheses:

(- a) = - a

= - d t cos (2 t)

sin (arctan (x - 2))

π sec (3 x + \frac{π}{2}) - 1

tan (arctan (\frac{x}{2}))

sin (\frac{1}{4} π + x)

sin (a) - sin (- a)

What is (sin^2(t)-cos^2(t))dt ?
The solution to (sin^2(t)-cos^2(t))dt is -cos(2t)dt