Question

How do you prove `10sin(x)cos(x)=6cos(x)`?

Answer 1

If we simplify the equation by dividing both sides by `cos(x)`, we obtain:

`10sin(x)=6`, which implies
`sin(x)=3/5.`

The right triangle which `sin(x)=3/5` is a 3:4:5 triangle, with legs `a=3`, `b=4` and hypotenuse `c=5`. From this we know that if `sin(x)=3/5` (opposite over hypotenuse), then `cos=4/5` (adjacent over hypotenuse). If we plug these identities back into the equation we reveal its validity:

`10(3/5)*(4/5)=6(4/5)`.

This simplifies to

`24/5=24/5`.

Therefore the equation is true for `sin(x)=3/5.`