\displaystyle 10{{\cos }^{2}}x+4{{\sin }^{2}}x+8\sin x\cos x
Split 10 cos2x and factorize 8sinxcosx.
\displaystyle 6{{\cos }^{2}}x+4{{\cos }^{2}}x+4{{\sin }^{2}}x+4\left( {2\sin x\cos x} \right)

Change 2sinxcosx to sin2x (Sine Double Angle Formula)

 

\displaystyle 3(2{{\cos }^{2}}x)+4({{\cos }^{2}}x+{{\sin }^{2}}x)+4\sin 2x

Change 2cos2x to cos2x+1 (Cosine Double Angle Formula)

 

\displaystyle 3(\cos 2x+1)+4+4\sin 2x

 

\displaystyle 7+4\sin 2x+3\cos 2x

 

\displaystyle R=\sqrt{{{{4}^{2}}+{{3}^{2}}}}=5

 

\displaystyle \tan \alpha =\frac{3}{4},\ \alpha ={{\tan }^{{-1}}}\frac{3}{4}={{36.9}^{o}}

 

\displaystyle y=7+5\left[ {\sin (2x+{{{36.9}}^{o}}} \right]

Additional Math (A Math) (a Math) Tuition in Woodlands and Johor Bahru.