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

1 Answer
May 19, 2018

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.