Evaluate :
` (cos 58 ^(@))/(sin 32^(@)) +(sin 22^(@))/(cos 68^(@)) - cos 90 ^(@) `

Answer

To evaluate the expression \( \frac{\cos 58^\circ}{\sin 32^\circ} + \frac{\sin 22^\circ}{\cos 68^\circ} - \cos 90^\circ \), we will follow these steps:

### Step 1: Rewrite the sine and cosine functions
We can use the co-function identities:
- \( \sin(90^\circ - \theta) = \cos(\theta) \)
- \( \cos(90^\circ - \theta) = \sin(\theta) \)

Using these identities, we rewrite \( \sin 32^\circ \) and \( \cos 68^\circ \):
- \( \sin 32^\circ = \sin(90^\circ - 58^\circ) = \cos 58^\circ \)
- \( \cos 68^\circ = \cos(90^\circ - 22^\circ) = \sin 22^\circ \)

### Step 2: Substitute the rewritten values
Now we substitute these identities back into the expression:
\[ \frac{\cos 58^\circ}{\sin 32^\circ} = \frac{\cos 58^\circ}{\cos 58^\circ} = 1 \]
\[ \frac{\sin 22^\circ}{\cos 68^\circ} = \frac{\sin 22^\circ}{\sin 22^\circ} = 1 \]

### Step 3: Substitute into the original expression
Now we can substitute these values back into the original expression:
\[ 1 + 1 - \cos 90^\circ \]

### Step 4: Evaluate \( \cos 90^\circ \)
We know that:
\[ \cos 90^\circ = 0 \]

### Step 5: Final calculation
Now we can complete the calculation:
\[ 1 + 1 - 0 = 2 \]

### Final Answer
The value of the expression is \( 2 \).

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