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[lyesya]

Hey. I'm in Pre-AP Calculus, and I'm in need of some help. I'm having a lot of trouble trying to figure out how my teacher got the answer.

Write an algebraic expression equivalent to
1. sin ( 2 arctan x)
I thought that you pull the 2 to the x and make x to the power of 2, but the answer is 2x/(1+x^2). I looked in the book, but I couldn't find problems

Comments

[misteral]

Have you tried drawing a right-angled triangle for each of these? For example, here's how I tackled question 1...

Draw the right-angled triangle with the shorter sides equal to 1 and x.

On the drawing, mark the angle θ which equals arctan x (= arctan (x/1)). Now you need to find sin 2θ.

Use Pythagoras to find the length of the hypotenuse in terms of x.

Use the triangle to write down expressions for sin θ and cos θ in terms of x.

Use the fact that sin 2θ = 2 sin θ cos θ to get the answer.

[lyesya]

No wonder I couldn't solve them, I completely forgot about the last identity! Thanks so much!