If $\mathrm{cosec} A=2$, then the value of $\cot$ $A+\frac{\sin A}{1+\cos A}$ is

What is the simplified value of: $\frac{{\sin }^3 {21}^{\circ }+{\cos }^3 {19}^{\circ }}{\sin {21}^{\circ }+\cos {19}^{\circ }}+{\sin }^2 {69}^{\circ }+{\cos }^2 {71}^{\circ }+\frac{1}{\sec {69}^{\circ }\mathrm{cosec} {71}^{\circ }}$ is

Which of the following is true?

The value of $\sec { }^{2}26°-\tan { }^{2}26°$ is

If $\cos \theta =\frac{2p}{p^2+1}$, $\left(p\ne \pm 1\right)$ then $\mathrm{cosec}\theta$ is equal to:

The value of $(\sin \theta + \cos \theta {)}^2=?$

1. $1+{\sin }^2\theta$
2. ${\sin }^2\theta +{\cos }^2\theta$ 
3.$1+2 \cos \theta \sin \theta$ 
4. ${\cos }^2 \theta + 1$