SOLUTION: use an identity to evaluate sin (2 invesre of sin 5/13)

Question 595833: use an identity to evaluate sin (2 invesre of sin 5/13)
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!

Broadly speaking this expression is a reference to the sin of twice some angle. This suggests that the identity to use is the one for sin(2x):
sin(2x) = 2*sin(x)*cos(x)

Applying this pattern to your expression we get:

is "the sine of the angle whose sin is 5/13". So it obviously has a value of 5/13.

is "the cosine of the angle whose sin is 5/13". Its value is not so obvious. To find it you can use the Pythagorean identity:

Substituting in our sin value this becomes:

To solve for cos(x) we start by simplifying:

Subtract the fraction:

Find the square root of each side (discarding the negative square root) we get:

Now that we have values for and we can substitute them into :

Simplifying we get:

This fraction does not reduce so

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