If $\text{cosec B} = \frac{\sqrt{3}}{2}$ and $A + B = 90^\circ$, then the value of sec A is :

Step 1: Analyze the given information

We are given the value of cosec B and a relationship between angles A and B. We need to find the value of sec A.

Step 2: Determine angle B

The cosecant function is the reciprocal of the sine function. Therefore, if $\text{cosec B} = \frac{\sqrt{3}}{2}$, then $\sin B = \frac{2}{\sqrt{3}}$. However, the sine of any real angle must be between -1 and 1, inclusive. Since $\frac{2}{\sqrt{3}} \approx 1.1547$, which is greater than 1, there is no real angle B for which $\sin B = \frac{2}{\sqrt{3}}$. This indicates an issue with the problem statement.

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