Which of the following are correct?

(1) cot(A+B) = $\frac{cotAcotB-1}{cotA+cotB}$

(2) cot(A-B) = $\frac{cotAcotB-1}{cotA-cotB}$

(3) tan(A+B) = $\frac{tanA+tanB}{1-tanAtanB}$

(4) tan(A-B) = $\frac{tanA-tanB}{1-tanAtanB}$

Q.

If a circle and rectangular hyperbola $xy=c^2$ meet in the four points $t_1,t_2,t_3\&t_4$ . Then which of the following statements are correct?
1. The center of the mean position of the four points bisects the distance between the center of the two curve.
2. Center of the circle through the points $t_1,t_2\&t_3$ is:$\left[\right(\frac{c}{2}(t_1+t_2+t_3)+\frac{1}{t_1.t_2.t_3}),\frac{c}{2}(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+t_1{t}_2{t}_3\left)\right]$

Q. Given that 2m-1 is an odd number and 3n-1 is an even number. Which of the following are necessarily odd? 1) $n^2-4m+52)m^2-2n+23)6m^2-n-1$

Q.

Which of the following statements is/are correct?

1. cos2A = $\frac{1+ta{n}^{2}A}{1-ta{n}^{2}A}$

2. $cose{c}^{2}A$ = 1 + $co{t}^2\theta$

3. $se{c}^2\theta$ = 1 + $co{s}^2\theta$

Q. Given that 2m-1 is an odd number and 3n-1 is an even number, which of the following are necessarily odd?
$1)n^2-4m+52)m^2-2n+23)6m^2-n-1$

Q. Which of the following molecules are polar: $O{F}_2,HF,S{O}_3$ ?