Evaulate : `(tan45^(@))/("cosec "30^(@))+(sec60^(@))/(cot45^(@))-(2sin90^(@))/(cos0^(@))`.

Answer

To evaluate the expression \( \frac{\tan 45^\circ}{\csc 30^\circ} + \frac{\sec 60^\circ}{\cot 45^\circ} - \frac{2 \sin 90^\circ}{\cos 0^\circ} \), we will calculate the trigonometric values step by step.

### Step 1: Calculate \( \tan 45^\circ \)
We know that:
\[ \tan 45^\circ = 1 \]

### Step 2: Calculate \( \csc 30^\circ \)
We know that:
\[ \csc 30^\circ = \frac{1}{\sin 30^\circ} = \frac{1}{\frac{1}{2}} = 2 \]

### Step 3: Calculate \( \sec 60^\circ \)
We know that:
\[ \sec 60^\circ = \frac{1}{\cos 60^\circ} = \frac{1}{\frac{1}{2}} = 2 \]

### Step 4: Calculate \( \cot 45^\circ \)
We know that:
\[ \cot 45^\circ = 1 \]

### Step 5: Calculate \( \sin 90^\circ \)
We know that:
\[ \sin 90^\circ = 1 \]

### Step 6: Calculate \( \cos 0^\circ \)
We know that:
\[ \cos 0^\circ = 1 \]

### Step 7: Substitute the values into the expression
Now substituting all the calculated values into the expression:
\[ \frac{\tan 45^\circ}{\csc 30^\circ} + \frac{\sec 60^\circ}{\cot 45^\circ} - \frac{2 \sin 90^\circ}{\cos 0^\circ} \]
becomes:
\[ \frac{1}{2} + \frac{2}{1} - \frac{2 \cdot 1}{1} \]

### Step 8: Simplify the expression
Now simplifying:
\[ \frac{1}{2} + 2 - 2 \]
\[ = \frac{1}{2} + 0 \]
\[ = \frac{1}{2} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{1}{2} \]