Solving a Trigonometric Equation: v^2*sin(180-2theta2)/g

[DeltaForce]

Homework Statement

Show that the range of the projectile is the same for two different projection angles --- a pair that add up to 90 degrees.

Relevant Equations

theta1 +theta2 = 90

v^2 * sin(2theta1)/g = v^2 *sin(2theta2)/g

theta1 = 90- theta2
I substituted that into v^2*sin(2theta1)/g
So I get
v^2*sin(180-2theta2)/g

Now I'm stuck. What do I do next?

 

[scottdave]

You need to go back to the equation. You need to show that the 2 sides of the equation are indeed equal, using some trigonometric identities. You may find this list of identities helpful. https://bitly.com/trigiden

 

[DeltaForce]

Ohh... ok. So it has something to do with the sum and difference identities. Thank you.

 

[haruspex]

What do I do next

You ought to know how to simplify sin(180-x), sin(90-x), sin(180+x), and likewise with cos.

 

[DeltaForce]

Yeah. I got it with the trig identities.