Find the value of :
`" "(sin30^(@)-sin90^(@)+2cos0^(@))/(tan30^(@) times tan60^(@))`

Answer

To solve the expression \((\sin 30^\circ - \sin 90^\circ + 2 \cos 0^\circ) / (\tan 30^\circ \times \tan 60^\circ)\), we will follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ \frac{\sin 30^\circ - \sin 90^\circ + 2 \cos 0^\circ}{\tan 30^\circ \times \tan 60^\circ} \]

### Step 2: Substitute the trigonometric values
Now, we will substitute the known values of the trigonometric functions:
- \(\sin 30^\circ = \frac{1}{2}\)
- \(\sin 90^\circ = 1\)
- \(\cos 0^\circ = 1\)
- \(\tan 30^\circ = \frac{1}{\sqrt{3}}\)
- \(\tan 60^\circ = \sqrt{3}\)

Substituting these values into the expression gives:
\[ \frac{\frac{1}{2} - 1 + 2 \times 1}{\frac{1}{\sqrt{3}} \times \sqrt{3}} \]

### Step 3: Simplify the numerator
Now, simplify the numerator:
\[ \frac{1}{2} - 1 + 2 = \frac{1}{2} - \frac{2}{2} + \frac{4}{2} = \frac{1 - 2 + 4}{2} = \frac{3}{2} \]

### Step 4: Simplify the denominator
Next, simplify the denominator:
\[ \frac{1}{\sqrt{3}} \times \sqrt{3} = 1 \]

### Step 5: Combine the results
Now we can combine the results from the numerator and denominator:
\[ \frac{\frac{3}{2}}{1} = \frac{3}{2} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{3}{2} \text{ or } 1.5 \]

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