The cosine function is an odd function true or false

Asked by admin @ 03/08/2021 in Math viewed by 354 People

True or false? Explain your answer. Because the sine function is an odd function, for a negative number u, sin 2u = -2 sin u cos u.

Answered by admin @ 03/08/2021

Given : Because the sine function is an odd function, for a negative number u, sin 2u = -2 sin u cos u.

To find : True or false

Solution:

Sin (2α) = 2 Sinα.Cosα

Let say if u is - ve then

let say u = - x where x is + ve

=> x = - u

Sin (2u )

= Sin ( -2x)

= - Sin(2x)

= - 2Sinx Cosx

Replacing x with - u

= - 2Sin(-u) Cos(-u)

Sin(-u) = - Sin u

Cos (-u) = Cos u

= - 2 (-Sin u) Cos u

= 2Sinu Cos u

Sin (2u ) = 2Sinu Cos u

Hence sin 2u = -2 sin u cos u. is False

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