Answer:
[tex]\frac{1+\sqrt{3}}{2\sqrt{2}}[/tex]
Step-by-step explanation:
We have to find the exact value of [tex]sin(\frac{7 \pi}{12} )[/tex] using the addition or subtraction rules.
This can be done as follows:
[tex]sin(\frac{7 \pi}{12}) = sin(\frac{3\pi + 4\pi}{12})[/tex]
Using the formula sin(A+B)=sin(A)cos(B) + cos(A)sin(B), the expression can be simplified to:
[tex]sin(\frac{3\pi + 4\pi}{12})\\\\ =sin(\frac{3 \pi}{12} )cos(\frac{4 \pi}{12} ) + cos(\frac{3 \pi}{12} )sin(\frac{4 \pi}{12} )\\\\ =sin(\frac{\pi}{4} )cos(\frac{\pi}{3} ) + cos(\frac{\pi}{4} )sin(\frac{\pi}{3})\\\\ = \frac{1}{\sqrt{2}} \times \frac{1}{2} + \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2}\\\\= \frac{1}{2\sqrt{2}}+\frac{\sqrt{3}}{2\sqrt{2}} \\\\ = \frac{1+\sqrt{3}}{2\sqrt{2}}[/tex]
