Trigonometric Identities and formulas There are so many identities like $\sin2θ$, $\cos2θ$, $\tan2θ$, $\sin(θ/2)$, $\cos(θ/2)$ and $\tan(θ/2)$. there are other formulas too like $\cos(α-β)$, $\sin(α-β)$ etc and yes the sum and product formulas of trigonometric function...
I am stuck in memorizing all. Is there any simple trick to memorize these formulas and identities?

For the multiple angle stuff it suffices to remember De Moivre's formula:
$$
    (\cos x + i \sin x)^n = \cos (nx) + i \sin (nx).\, 
$$
With it you easily get 
$$
    \begin{align}(\cos x + i \sin x)^2 &= \cos^2 x + 2i\sin x \cos x - \sin^2 x = (\cos^2 x - \sin^2 x) + i(2 \sin x \cos x)\\ &= \cos(2x) + i \sin (2x)\end{align} 
$$
and then 
$$
    \cos^2 x - \sin^2 x = \cos(2x) \\
    2\sin x \cos x = \sin(2x) . 
$$
by comparing real and imaginary parts...
Sums and differences can be written in Matrix Form:
$$
    \begin{align} & {} \quad \left(\begin{array}{rr} \cos\alpha & -\sin\alpha \\ \sin\alpha & \cos\alpha \end{array}\right) \left(\begin{array}{rr} \cos\beta & -\sin\beta \\ \sin\beta & \cos\beta \end{array}\right) \\[12pt] & = \left(\begin{array}{rr} \cos\alpha\cos\beta - \sin\alpha\sin\beta & -\cos\alpha\sin\beta - \sin\alpha\cos\beta \\ \sin\alpha\cos\beta + \cos\alpha\sin\beta & -\sin\alpha\sin\beta + \cos\alpha\cos\beta \end{array}\right) \\[12pt] & = \left(\begin{array}{rr} \cos(\alpha+\beta) & -\sin(\alpha+\beta) \\ \sin(\alpha+\beta) & \cos(\alpha+\beta) \end{array}\right). \end{align} 
$$
