Question

Sin(α2) + cos(α2) = 1
True or false

Answer 1

FALSE sin(α^2) + cos(α^2) = 1 is FALSE. It's attempting to trick you by resembling a different identity of: sin(α)^2 + cos(α)^2 = 1 which is quite true. To illustrate, you can have the expression x = α^2 and substitute it into the expression, getting sin(x) + cos(x) = 1 which you should recognize as being false.

Answer 2

Sin (α ^ 2) + cos (α ^ 2) = 1
False
To solve the problem let's make the following change of variables:
x = α ^ 2
We substitute in the original equation:
Sin (x) + cos (x) = 1
We observe that the trigonometric equation is false.
The trigonometric identity that is equal to one is the sum of the sine to the square of an angle plus the cosine to the square of the same angle. In other words, mathematically it is written as:
(Sin (α)) ^ 2 + (cos (α)) ^ 2 = 1
answer
false