# Thread: Trig proof - urg

1. ## Trig proof - urg

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

Hence, prove that the only real solution of the equation
$\displaystyle Sin 7 \theta = 7Sin\theta$
are given by
$\displaystyle \theta = n\pi$
Where n is an integer.
I am really stuck with this

Any help would be greatly appreciated.
Thankyou.

2. Math Forum - Ask Dr. Math

3. Originally Posted by bebrave
Math Forum - Ask Dr. Math
4. Use what you just proved. Substitute , substract $\displaystyle 7\sin(\theta)$.
You then have $\displaystyle 64\sin^7(\theta)-112\sin^5(\theta)+56\sin^3(\theta)=0$.
Use what you just proved. Substitute , substract $\displaystyle 7\sin(\theta)$.
You then have $\displaystyle 64\sin^7(\theta)-112\sin^5(\theta)+56\sin^3(\theta)=0$.
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