Answer
a): It is an identity because $(x+y)^2$ is exactly $x^2 +2x y + y^2$, and we can try any two numbers to check. For example; $x=2, y=5$, we get from both sides the answer $2^2+2*2*5+5^2 = 7^2= 49$.
b): It is not identity, because it is true for all numbers on the unit circle only.
c): It is identity, because it is exactly the distribution law. It looks like a common factor distributed on addition.
d): It is identity, because it is exactly a difference between two square items. The rule is $(a^2 - b^2) = (a-b)(a+b)$.
e): It is not identity, because (as an example) $sin30 +cos30 \neq 1$. The correct identity is $sin^2 (z) +cos^2 (z) = 1 \ \forall z \in R$.
f): It is not identity, because it is not true at all values of $x$. For example $45^2 - tan^2 (45) = 45^2-1 \neq 0.$
Work Step by Step
a): It is an identity because $(x+y)^2$ is exactly $x^2 +2x y + y^2$, and we can try any two numbers to check. For example; $x=2, y=5$, we get from both sides the answer $2^2+2*2*5+5^2 = 7^2= 49$.
b): It is not identity, because it is true for all numbers on the unit circle only.
c): It is identity, because it is exactly the distribution law. It looks like a common factor distributed on addition.
d): It is identity, because it is exactly a difference between two square items. The rule is $(a^2 - b^2) = (a-b)(a+b)$.
e): It is not identity, because (as an example) $sin30 +cos30 \neq 1$. The correct identity is $sin^2 (z) +cos^2 (z) = 1 \ \forall z \in R$.
f): It is not identity, because it is not true at all values of $x$. For example $45^2 - tan^2 (45) = 45^2-1 \neq 0.$
