Question 816020
{{{ 4sin^2(7t)cos^2(7t) }}}
Recognizing that the sin(2x) identity is buried in there is more than half the battle! Very good!<br>
Now we just have to see how we can use it. Yes, the sin and cos in your expression are squared. But isn't 4 also the square of the 2? So isn't your expression just the square of sin(2x)?:
{{{(2sin(7t)cos(7t))^2}}}
Now we can use the sin(2x) formula with 7t in the place of x:
{{{(sin(2(7t)))^2}}}
The argument simplifies:
{{{(sin(14t))^2}}}
which can also be written as:
{{{sin^2(14t)}}}