Trigonometry

The value of $\cos{80}^{\circ}\cos{20}^{\circ}+\sin{80}^{\circ}\sin{20}^{\circ}=$

The value of the expression $\tan (x-9 \pi)$ is equal to:

The value of $\sin{70}^{\circ}\cos{10}^{\circ}-\cos{70}^{\circ}\sin{10}^{\circ}$ is equal to

The value of $\dfrac{1+\cos\theta}{\sin\theta}$ is equal to

$2\sin 3\theta\sin\theta=$

$\sin 4\theta+\sin 2\theta=$

The value of $\sqrt{2}\sin\left( \dfrac{\pi}{4}-\theta\right)$ is

The value of $\tan{840}^{\circ}$ is equal to

The value of $\sin 2A(\tan A+\cot A)$ is equal to

The maximum value of the function $a \sin x+b \cos x$ is

$\sin\left( \theta-\dfrac{\pi}{6} \right)+\cos\left( \theta-\dfrac{\pi}{3} \right)=$

$\dfrac{\sin\left( {90}^{\circ}+A \right)}{\cos(-A)}-\dfrac{\sin\left( {180}^{\circ}-A \right)}{\sin(-A)}+\dfrac{\tan\left( {270}^{\circ}+A \right)}{\cot(-A)}=$

If $\tan x=\dfrac{3}{4}$ and $\pi<x<\dfrac{3\pi}{2}$, then $\cos\dfrac{x}{2}=$ $\_\_\_\_$

If $\cos 43^{\circ}+\sin 43^{\circ}=k^{3}$, then $\cos 2^{\circ}=\ldots$.

If $x+y=\dfrac{\pi}{4}$, then $(1+\tan x)(1+\tan y)=$