If `sinx+cosy=1" and "x=30^(@)`, find the value of y.

Answer

To solve the problem step by step, we will follow the given equation and the provided information.

### Step 1: Write down the given equation
We are given the equation:
\[ \sin x + \cos y = 1 \]
and we know that:
\[ x = 30^\circ \]

### Step 2: Substitute the value of x into the equation
Substituting \( x = 30^\circ \) into the equation gives us:
\[ \sin(30^\circ) + \cos y = 1 \]

### Step 3: Calculate \( \sin(30^\circ) \)
We know from trigonometric ratios that:
\[ \sin(30^\circ) = \frac{1}{2} \]

### Step 4: Substitute \( \sin(30^\circ) \) into the equation
Now substituting \( \sin(30^\circ) = \frac{1}{2} \) into the equation gives us:
\[ \frac{1}{2} + \cos y = 1 \]

### Step 5: Isolate \( \cos y \)
To isolate \( \cos y \), we subtract \( \frac{1}{2} \) from both sides:
\[ \cos y = 1 - \frac{1}{2} \]
\[ \cos y = \frac{1}{2} \]

### Step 6: Find the angle y
We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]
Thus, we can conclude that:
\[ y = 60^\circ \]

### Final Answer
The value of \( y \) is:
\[ y = 60^\circ \]

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