I'm trying to verify the identity: (sin^2 x)/(2)= (secx-1)/(2secx)
To verify the identity:
(sin^2 x) / 2 = (secx - 1) / (2secx)
We'll start by working on the left-hand side (LHS) of the equation and try to simplify it:
(sin^2 x) / 2
Since sin^2 x is equivalent to (1 - cos^2 x), we can rewrite the LHS as:
(1 - cos^2 x) / 2
Now, let's work on the right-hand side (RHS) of the equation:
(secx - 1) / (2secx)
Recall that secx is the reciprocal of cosx, so we can rewrite the RHS as:
(1/cosx - 1) / (2/cosx)
Now, let's simplify the RHS by combining the fractions:
[1 - (cosx/cosx)] / (2/cosx)
Simplifying further:
(1 - 1) / (2/cosx) [since cosx/cosx equals 1]
0 / (2/cosx)
Since anything divided by zero is undefined, the RHS is undefined.
So, the equation is not an identity, as the LHS is defined, but the RHS is undefined.