Please help to solve this: y=cos^2x - sin^2x

I don't know how to differentiate it. Thanks.

Printable View

- Apr 2nd 2013, 03:10 PMonehundredpercenteffortsinusoidal differentiation
Please help to solve this: y=cos^2x - sin^2x

I don't know how to differentiate it. Thanks. - Apr 2nd 2013, 03:43 PMfrankitmRe: sinusoidal differentiation
Assuming that the function is y =cos^2(x)-sin^2(x)

y´= y´(cos^2(x))-y´(sin^2(x))

y´= 2cosx(-sinx)- 2sinx(cosx)

y´= -2sinxcosx-2sinxcosx

y´= -4sinxcosx

frank - Apr 2nd 2013, 04:09 PMonehundredpercenteffortRe: sinusoidal differentiation
thanks for replying. However, the back of the book has a different answer: -2sin2x

could you clarify? Thanks - Apr 2nd 2013, 04:21 PMfrankitmRe: sinusoidal differentiation
That´s because sin2x = 2sinxcosx (by double angle trigonometric identity)

then

-2sin2x = -2(2sinxcosx) = -4sinxcosx, and thats all. - Apr 2nd 2013, 04:27 PMonehundredpercenteffortRe: sinusoidal differentiation
thanks