Question

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.

Answer 1

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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Answer 2

The answer is actually TRUE !