Question

what is sin 105°+cos 105° equal to?

Answer 1

Heya frnd...

Here is ur answer...

sin(60+45) + cos(60+45)

=[sin60cos45 +cos60sin45] + [cos60 cos45 - sin60sin45]

=cos 60 sin 45 +cos60 cos45

=1/2 * 1/sqrt2 + 1/2 * 1/sqrt2

=1/sqrt2

cos45°

Hope it helps u☺

Answer 2

Answer:

Option c - $\sin 105^{\circ}+\cos 105^{\circ}=\frac{1}{\sqrt2}$

Step-by-step explanation:

Given : Expression $\sin 105^{\circ}+\cos 105^{\circ}$

To find : The expression is equal to ?

Solution :

We can write the expression as,

$\sin 105^{\circ}+\cos 105^{\circ}=\sin \left(60^{\circ}+45^{\circ}\right)+\cos \left(60^{\circ}+45^{\circ}\right)$

We know,

$\sin(A+B)=\sin A\cos B+\cos A\sin B$

$\cos(A+B)=\cos A\cos B-\sin A\sin B$

Applying the identity,

$=(\sin60^\circ\cos45^\circ+\cos60^\circ\sin45^\circ)+(\cos60^\circ \cos45^\circ-\sin60^\circ\sin45^\circ)$

We know, $\sin 60^\circ=\frac{\sqrt{3}}{2}$ and $\sin 45^\circ=\frac{1}{\sqrt{2}}$

$\cos 60^\circ=\frac{1}{2}$ and $\cos 45^\circ=\frac{1}{\sqrt{2}}$

Substitute in expression,

$=((\frac{\sqrt{3}}{2})(\frac{1}{\sqrt{2}})+(\frac{1}{2})(\frac{1}{\sqrt{2}}))+((\frac{1}{2})(\frac{1}{\sqrt{2}})-(\frac{\sqrt{3}}{2})(\frac{1}{\sqrt{2}}))$

$=\frac{\sqrt{3}}{2\sqrt2}+\frac{1}{2\sqrt2}+\frac{1}{2\sqrt2}-\frac{\sqrt{3}}{2\sqrt2}$

$=\frac{2}{2\sqrt2}$

$=\frac{1}{\sqrt2}$

Therefore, $\sin 105^{\circ}+\cos 105^{\circ}=\frac{1}{\sqrt2}$

So, Option 'c' is correct.