Given $sin\alpha=\frac{\sqrt{3}}{2}$ and $cos\beta=0$, then find the value of $( \beta-\alpha)$.

Given: $sin\alpha=\frac{\sqrt{3}}{2}$ and $cos\beta=0$.

To do: To find the value of $( \beta-\alpha)$.

Solution:

As given,

$sin\alpha=\frac{\sqrt{3}}{2}$

$\Rightarrow \alpha=60^o$

And  $cos\beta=0$

$\Rightarrow \beta=90^o$

$\therefore \beta-\alpha=90^o-60^o$

$\Rightarrow \beta-\alpha=30^o$

Thus, the value of $( \beta-\alpha)$ is $30^o$.