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.#