Question

Find \sin\left(\dfrac{7\pi}{12}\right)sin( 12 7π ​ )sine, left parenthesis, start fraction, 7, pi, divided by, 12, end fraction, right parenthesis exactly using an angle addition or subtraction formula.

Answer 1

Answer: The correct answer is 12 over 37 for khan Academy.

Explanation:

Answer 2

`(1+√(3))/(2√(2))`

Explanation:

We have to find the exact value of
`sin((7 \pi)/(12) )` using the addition or subtraction rules.

This can be done as follows:

`sin((7 \pi)/(12)) = sin((3\pi + 4\pi)/(12))`

Using the formula sin(A+B)=sin(A)cos(B) + cos(A)sin(B), the expression can be simplified to:

`sin((3\pi + 4\pi)/(12))\\\\ =sin((3 \pi)/(12) )cos((4 \pi)/(12) ) + cos((3 \pi)/(12) )sin((4 \pi)/(12) )\\\\ =sin((\pi)/(4) )cos((\pi)/(3) ) + cos((\pi)/(4) )sin((\pi)/(3))\\\\ = (1)/(√(2)) * (1)/(2) + (1)/(√(2)) * (√(3))/(2)\\\\= (1)/(2√(2))+(√(3))/(2√(2)) \\\\ = (1+√(3))/(2√(2))`