To solve this equation, we can first simplify it by distributing the 8 to both terms inside the parentheses:
8cosy - 56/siny + 1 = 0
Next, we can move the 56/siny to the other side of the equation by adding it to both sides:
8cosy + 1 = 56/siny
Now, we can get rid of the fraction by multiplying both sides by siny:
siny(8cosy + 1) = 56
Expanding the left side:
8cosy(siny) + siny = 56
Using the trigonometric identity cos(x)sin(x) = 1/2sin(2x), we get:
4sin(2y) + siny = 56
Now, let's rearrange the equation to isolate the siny term:
siny(4cosy + 1) = 56
Finally, we can solve for siny:
siny = 56 / (4cosy + 1)
To solve this equation, we can first simplify it by distributing the 8 to both terms inside the parentheses:
8cosy - 56/siny + 1 = 0
Next, we can move the 56/siny to the other side of the equation by adding it to both sides:
8cosy + 1 = 56/siny
Now, we can get rid of the fraction by multiplying both sides by siny:
siny(8cosy + 1) = 56
Expanding the left side:
8cosy(siny) + siny = 56
Using the trigonometric identity cos(x)sin(x) = 1/2sin(2x), we get:
4sin(2y) + siny = 56
Now, let's rearrange the equation to isolate the siny term:
siny(4cosy + 1) = 56
Finally, we can solve for siny:
siny = 56 / (4cosy + 1)