[tex]7\cos \left(2x\right)[/tex]
1) The point here is to use a double-angle formula, so let's pick this double-angle identity below:
[tex]1-2\sin ^2\left(x\right)=\cos \left(2x\right)[/tex]
2) Now, let's rewrite that expression by making use of that expression above, and factoring it:
[tex]\begin{gathered} 7-14\sin^2\left(x\right)\:\:\: \\ \\ 7\cdot \:1-7\cdot \:2\sin ^2\left(x\right) \\ \\ 7\left(1-2\sin ^2\left(x\right)\right) \\ \\ \left(1-2\sin^2\left(x\right)\right)7\:\:\:Use\:this\:double\:angle\:identity:\:1-2\sin^2\left(x\right)=\cos\left(2x\right) \\ \\ (\cos(2x))7 \\ \\ 7\cos \left(2x\right) \end{gathered}[/tex]
Note that we could simplify that since at the end, we could match it with the formula above.
