Given:
The value is [tex]\dfrac{\sqrt{2}}{2}[/tex].
To find:
The values from the given options which are equal to the given value.
Solution:
We have,
[tex]\dfrac{\sqrt{2}}{2}[/tex]
It can be written as:
[tex]\dfrac{\sqrt{2}}{2}=\dfrac{1}{\sqrt{2}}[/tex]
From the standard trigonometric table, we get
[tex]\sin 30^\circ=\dfrac{1}{2}[/tex]
[tex]\sin 45^\circ=\dfrac{1}{\sqrt{2}}[/tex]
[tex]\cos 45^\circ=\dfrac{1}{\sqrt{2}}[/tex]
[tex]\cos 60^\circ=\dfrac{1}{2}[/tex]
[tex]\tan 30^\circ=\dfrac{1}{\sqrt{3}}[/tex]
[tex]\tan 45^\circ=1[/tex]
From the above values it is clear that the value of [tex]\sin 45^\circ [/tex] and [tex]\cos 45^\circ [/tex] are equal to [tex]\dfrac{1}{\sqrt{2}}[/tex].
Therefore, [tex]\sin 45^\circ [/tex] and [tex]\cos 45^\circ [/tex] and equal to [tex]\dfrac{\sqrt{2}}{2}[/tex]. So, options B and C are correct.
