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.

I think you have a typo. As written, the equation does not hold. Try using x=pi/4. Check to see whether you need exponents on the secx terms.