Question

Value of $sin\left({105}^{\circ }\right)+cos\left({105}^{\circ }\right)$ will be-

• A. $\frac{1}{2}$
• B. $\frac{3}{2}$
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{2}}$

$\sin {105}^{\circ }=\sin ({60}^{\circ }+{45}^{\circ })=\sin {60}^{\circ }\cos {45}^{\circ }+\cos {60}^{\circ }\sin {45}^{\circ }=\frac{\sqrt{3}+1}{2\sqrt{2}}$

$\cos {105}^{\circ }=\cos ({60}^{\circ }+{45}^{\circ })=\cos {60}^{\circ }\cos {45}^{\circ }-\sin {60}^{\circ }\sin {45}^{\circ }=\frac{1-\sqrt{3}}{2\sqrt{2}}$

$\sin {105}^{\circ }+\cos {105}^{\circ }=\frac{1+\sqrt{3}}{2\sqrt{2}}+\frac{1-\sqrt{3}}{2\sqrt{2}}=\frac{1}{\sqrt{2}}$