Question

sin15 + cos 15



the answer is √2/√3 but how to get it I need explanation

plz give correct answer.

Answer 1

Answer:

Step-by-step explanation:

We have,

$\rm{sin\left(15^{\circ}\right)+cos\left(15^{\circ}\right)}$

$\rm{=\sqrt{2}\cdot\left\{\dfrac{1}{\sqrt{2}}\cdot\,sin\left(15^{\circ}\right)+\dfrac{1}{\sqrt{2}}\cdot\,cos\left(15^{\circ}\right)\right\}}$

$\rm{=\sqrt{2}\cdot\big\{cos\left(45^{\circ}\right)\cdot\,sin\left(15^{\circ}\right)+sin\left(45^{\circ}\right)\cdot\,cos\left(15^{\circ}\right)\big\}}$

$\rm{=\sqrt{2}\cdot\big\{sin\left(15^{\circ}\right)\cdot\,cos\left(45^{\circ}\right)+cos\left(15^{\circ}\right)\cdot\,sin\left(45^{\circ}\right)\big\}}$

$\rm{=\sqrt{2}\cdot\,sin\left(15^{\circ}+45^{\circ}\right)}$

$\rm{=\sqrt{2}\cdot\,sin\left(60^{\circ}\right)}$

$\rm{=\sqrt{2}\cdot\dfrac{\sqrt{3}}{2}}$

$\rm{=\sqrt{2}\cdot\dfrac{\sqrt{3}}{\sqrt{2}\cdot\sqrt{2}}}$

$\rm{=\dfrac{\sqrt{3}}{\sqrt{2}}}$