# Find the value of $\sin25^° \sin35^° \sin85^°$

Trigo problem :

Find the value of $\sin25^° \sin35^° \sin85^°$.

My approach :

Using $2\sin A\sin B = \cos(A-B) -\cos(A+B)$

\begin{align} & \phantom{={}}[\cos10^{°} -\cos60^°] \sin85^° \\ & = \frac{1}{2}[2\cos10^°\sin85^° -2\cos60^° \sin85^°] \\ & = \frac{1}{2}[2\cos10^°\sin85^° -2 \frac{1}{2} \sin85^°] \\ & = \frac{1}{2}[2\cos10^°\sin85^° -\sin85^°] \\ & = \frac{1}{2} [\sin 95^° + \sin 75^° -\sin85^°] \end{align}

After this I am unable to solve further.... please guide... thanks.

Note that $\sin(95^\circ)=\sin(85^\circ)$.
We can get an explicit formula for $\sin(75^\circ)$ in various ways, probably most simply by writing it as $\sin(30^\circ+45^\circ)$ and using the Addition Law.
• oh! got it thanks.. I skipped that cancellation of sin $95^{\circ}$ and $sin85^{\circ}$ .. thanks once againthanks.. – sachin Sep 30 '13 at 3:41