Question

Can you please help? The question is in the picture picture. thank you

Answer 1

Given:

The value is $\dfrac{\sqrt{2}}{2}$.

To find:

The values from the given options which are equal to the given value.

Solution:

We have,

$\dfrac{\sqrt{2}}{2}$

It can be written as:

$\dfrac{\sqrt{2}}{2}=\dfrac{1}{\sqrt{2}}$

From the standard trigonometric table, we get

$\sin 30^\circ=\dfrac{1}{2}$

$\sin 45^\circ=\dfrac{1}{\sqrt{2}}$

$\cos 45^\circ=\dfrac{1}{\sqrt{2}}$

$\cos 60^\circ=\dfrac{1}{2}$

$\tan 30^\circ=\dfrac{1}{\sqrt{3}}$

$\tan 45^\circ=1$

From the above values it is clear that the value of $\sin 45^\circ$ and $\cos 45^\circ$ are equal to $\dfrac{1}{\sqrt{2}}$.

Therefore, $\sin 45^\circ$ and $\cos 45^\circ$ and equal to $\dfrac{\sqrt{2}}{2}$. So, options B and C are correct.