06. Trigonometric Ratios, Functions and Identities question bank (Maths)

If  
\[
\cos (\alpha + \beta) + \sin (\alpha - \beta) = 0 
\quad \text{and} \quad 
2010 \tan \beta + 1 = 0,
\]  
then \(\tan \alpha\) is equal to:  

If  
\[
A = \tan 6^{\circ} \tan 42^{\circ} 
\quad \text{and} \quad 
B = \cot 66^{\circ} \cot 78^{\circ},
\]
then: