List I (Trigonometric equation)	List II(General Solution)
A)  $\cos 2\theta =\frac{\sqrt{5}+1}{4}$	P) $\theta =n\pi \pm \frac{\pi }{3},n\in z$
B)  $Ta{n}^2\theta =3$	Q) $\theta =2n\pi \pm \frac{\pi }{4}+\frac{\pi }{6},n\in z$
C)  $2{\sin }^2\theta =3\cos \theta$	R)  $\theta =n\pi \pm \frac{\pi }{10},n\in z$
d)  $\sqrt{3}\cos \theta +\sin \theta =\sqrt{2}$	S) $\theta =2n\pi \pm \frac{\pi }{3},n\in z$

$\left(a\right)\cos 2\theta =\frac{\sqrt{5}+1}{4}$

$\cos 2\theta =\cos \frac{\pi }{5}$

$\theta =n\pi \pm \frac{\pi }{10},n\in z$

$\left(b\right){\mathrm{Tan}}^2\theta =3$

$\Rightarrow {\mathrm{Tan}}^2\theta ={\mathrm{Tan}}^2\frac{\pi }{3}$

$\theta =n\pi \pm \frac{\pi }{3},n\in z$

$\left(c\right)2{\sin }^2\theta =3\cos \theta$

$2\left(1-{\cos }^2\theta \right)=3\cos \theta$

$\Rightarrow 2{\cos }^2\theta +3\cos \theta -2=0$

$\left(\cos \theta +2\right)\left(2\cos \theta -1\right)=0$

$\cos \theta =\frac{1}{2}$

$\theta =2n\pi \pm \frac{\pi }{3},n\in z$

$\left(d\right)\sqrt{3}\cos \theta +\sin \theta =\sqrt{2}$

$\frac{\sqrt{3}}{2}\cos \theta +\frac{1}{2}\sin \theta =\frac{1}{\sqrt{2}}$

$\cos \left(\theta -\frac{\pi }{6}\right)=\cos \frac{\pi }{4}$

$\theta -\frac{\pi }{6}=2n\pi \pm \frac{\pi }{4}$

$\Rightarrow \theta =2n\pi \pm \frac{\pi }{4}+\frac{\pi }{6},n\in z$