What makes a mathemathical statement sinx=cosxtanx an identity when statement sinx=1/2 is not an identity?

Answer 1

same reason that x=x is an identity
but x=1/2 is not

whatever value you put in for an unknown in an identity makes it true but for a solutin like x=1/2 or sinx=1/2 only certain values for x make it true

like sin30 degrees =1/2
but sin 45 does not
but sin30=cos30tan30
and sin 45=cos45tan 45
and on and on for any value of x
except where tan is undefined

Answer 2

An identity is a statement that's true for every value of the variable. So in the first sentence, it doesn't matter which x you choose, they will all have that property. In the second statement, sinx=1/2 is only true for particular values of x, like 30 degrees. It's not true for every x, just try 0 or 1.

Answer 3

Value of theta in first case is immaterial to prove the statement to be true. But in second case x has only finite number of values like pi/6, 2pi/3, and so on.

Answer 4

Because sin x = cos x tan x regardless of what the value of x is (provided that both expressions are defined, anyway). Whereas sin x = 1/2 is only true for a few particular values of x.

Answer 5

:-o say what!!