# Math Help - Trig proof - urg

1. ## Trig proof - urg

It is given that:
$
Sin7\theta = 7Sin{\theta} - 56Sin^3\theta + 112Sin^5\theta - 64Sin^7\theta
$

Hence, prove that the only real solution of the equation
$Sin 7 \theta = 7Sin\theta$
are given by
$
\theta = n\pi
$

Where n is an integer.
I am really stuck with this

Any help would be greatly appreciated.
Thankyou.

2. Math Forum - Ask Dr. Math
this link can help you

3. Originally Posted by bebrave
Math Forum - Ask Dr. Math
this link can help you
Thankyou very much for your reply however im find with putting Sin 7x into the equation by demoivres , that was the first part of the question which i managed ...its the proof part im struggling with .

4. Use what you just proved. Substitute , substract $7\sin(\theta)$.
You then have $64\sin^7(\theta)-112\sin^5(\theta)+56\sin^3(\theta)=0$.
Show that has no real roots other than 0.

5. Originally Posted by Plato
Use what you just proved. Substitute , substract $7\sin(\theta)$.
You then have $64\sin^7(\theta)-112\sin^5(\theta)+56\sin^3(\theta)=0$.
Show that has no real roots other than 0.
Plato, you're awsome! Thanks again for another reply