Question

Evaluate the value of $\sin 45^\circ + \cos 45^\circ $ .

Answer 1

Hint:
Here, it is asked to find the value of $\sin 45^\circ + \cos 45^\circ $.
So, firstly, find the values of $\sin 45^\circ $ and $\cos 45^\circ $.
Thus, on obtaining the values of $\sin 45^\circ $ and $\cos 45^\circ $ , substitute the values in the given equation.
Hence, the required answer is obtained.

Complete step by step solution:
Here, we are asked to find the value of $\sin 45^\circ + \cos 45^\circ $ .
To do so, we firstly need the values of $\sin 45^\circ $ and $\cos 45^\circ $ .
We know that, $\sin 45^\circ = \dfrac{1}{{\sqrt 2 }}$ and $\cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$ .
Now, substituting $\sin 45^\circ = \dfrac{1}{{\sqrt 2 }}$ and $\cos 45^\circ = \dfrac{1}{{\sqrt 2 }}$ in the given trigonometric equation.
 $\therefore \sin 45^\circ + \cos 45^\circ = \dfrac{1}{{\sqrt 2 }} + \dfrac{1}{{\sqrt 2 }}$
$
   = \dfrac{{1 + 1}}{{\sqrt 2 }} \\
   = \dfrac{2}{{\sqrt 2 }} \\
   = \sqrt 2
$

Thus, we get the value of $\sin 45^\circ + \cos 45^\circ $ as $\sqrt 2 $.

Note:
Some useful values to be remembered:

	$0^\circ $	$30^\circ $	$45^\circ $	$60^\circ $	$90^\circ $
$\sin \theta $	0	$\dfrac{1}{2}$	$\dfrac{1}{{\sqrt 2 }}$	$\dfrac{{\sqrt 3 }}{2}$	1
$\cos \theta $	1	$\dfrac{{\sqrt 3 }}{2}$	$\dfrac{1}{{\sqrt 2 }}$	$\dfrac{1}{2}$	0
$\tan \theta $	0	$\dfrac{1}{{\sqrt 3 }}$	1	\[\sqrt 3 \]	Not defined
$\operatorname{cosec} \theta $	Not defined	2	$\sqrt 2 $	$\dfrac{2}{{\sqrt 3 }}$	1
$\sec \theta $	1	$\dfrac{2}{{\sqrt 3 }}$	$\sqrt 2 $	2	Not defined
$\cot \theta $	Not defined	\[\sqrt 3 \]	1	$\dfrac{1}{{\sqrt 3 }}$	0