To simplify the expression sin^18 - cos^18 / 10 tan(27) sin^117, we can start by breaking down each term.
Let's start with sin^18 - cos^18. We can rewrite this as (sin^2)^9 - (cos^2)^9. Using the Pythagorean identity sin^2 + cos^2 = 1, we can rewrite sin^18 - cos^18 as (1 - cos^2)^9 - cos^18.
Next, we can simplify the expression 10 tan(27). Since tan(27) is not a standard value, we cannot simplify this further at the moment.
Finally, we have sin^117. We can rewrite this as (sin^2)^58. Using the Pythagorean identity sin^2 + cos^2 = 1, we have sin^117 = (1 - cos^2)^58.
Putting it all together, the expression simplifies to:
To simplify the expression sin^18 - cos^18 / 10 tan(27) sin^117, we can start by breaking down each term.
Let's start with sin^18 - cos^18. We can rewrite this as (sin^2)^9 - (cos^2)^9. Using the Pythagorean identity sin^2 + cos^2 = 1, we can rewrite sin^18 - cos^18 as (1 - cos^2)^9 - cos^18.
Next, we can simplify the expression 10 tan(27). Since tan(27) is not a standard value, we cannot simplify this further at the moment.
Finally, we have sin^117. We can rewrite this as (sin^2)^58. Using the Pythagorean identity sin^2 + cos^2 = 1, we have sin^117 = (1 - cos^2)^58.
Putting it all together, the expression simplifies to:
((1 - cos^2)^9 - cos^18) / (10 tan(27) * (1 - cos^2)^58)