Evaluate :
`cosec(65^(@)+A)-sec(25^(@)-A)`

Answer

To evaluate the expression \( \csc(65^\circ + A) - \sec(25^\circ - A) \), we can follow these steps:

### Step 1: Use the co-function identity
We know from trigonometric identities that:
\[ \sec(90^\circ - \theta) = \csc(\theta) \]
In our case, we can express \( \csc(65^\circ + A) \) in terms of secant:
\[ \csc(65^\circ + A) = \sec(90^\circ - (65^\circ + A)) = \sec(25^\circ - A) \]

### Step 2: Substitute the identity into the expression
Now, substitute this identity back into the original expression:
\[ \csc(65^\circ + A) - \sec(25^\circ - A) = \sec(25^\circ - A) - \sec(25^\circ - A) \]

### Step 3: Simplify the expression
Now, we can see that:
\[ \sec(25^\circ - A) - \sec(25^\circ - A) = 0 \]

### Final Answer
Thus, the evaluated expression is:
\[ \boxed{0} \]

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