Question 1161416
<pre>
{{{sin(8theta)-sin(10theta) = cot(9theta)(cos(10theta)-cos(8theta))}}}

We work with the left side only first:

{{{sin(8theta)-sin(10theta)}}}

Rewrite 8θ as 9θ-θ and 10θ as 9θ+θ

{{{sin(9theta-theta)-sin(9theta+theta)}}}

{{{(sin(9theta)cos(theta)-cos(9theta)sin(theta)^"")-(sin(9theta)cos(theta)+cos(9theta)sin(theta)^"")}}}

{{{sin(9theta)cos(theta)-cos(9theta)sin(theta)-sin(9theta)cos(theta)-cos(9theta)sin(theta)}}}

{{{cross(sin(9theta)cos(theta))-cos(9theta)sin(theta)-cross(sin(9theta)cos(theta))-cos(9theta)sin(theta)}}}

{{{-2cos(9theta)sin(theta)}}}

Now we work with the right side only:

{{{cot(9theta)(cos(10theta)-cos(8theta))}}}

Rewrite 8θ as 9θ-θ and 10θ as 9θ+θ

{{{cot(9theta)(cos(9theta+theta)-cos(9theta-theta))}}}

{{{cot(9theta)(

(cos(9theta)cos(theta)-sin(9theta)sin(theta)^"")

-(cos(9theta)cos(theta)+sin(9theta)sin(theta)^"")^""


)}}}

{{{cot(9theta)(

cos(9theta)cos(theta)-sin(9theta)sin(theta)^""

-cos(-9theta)cos(theta)-sin(9theta)sin(theta)^""


)}}}

{{{cot(9theta)(

cross(cos(9theta)cos(theta))-sin(9theta)sin(theta)^""

-cross(cos(-9theta)cos(theta))-sin(9theta)sin(theta)^""


)}}}

{{{cot(9theta)(-2sin(9theta)sin(theta)^"") }}}

{{{(cos(9theta)/sin(9theta))(-2sin(9theta)sin(theta)^"") }}}

{{{(cos(9theta)/cross(sin(9theta)))(-2cross(sin(9theta))sin(theta)^"") }}}

{{{-2cos(9theta)sin(theta)}}}

Both sides work down the same expression.

Edwin</pre>