Simplify the following expression by using identities.
\(\frac{{{{\sin }^2}{\rm{x}} - 1}}{{\sin {\rm{x\;}} + {\rm{\;}}1{\rm{\;}}}}\)
$(\because 1 - {\sin ^2}x = \left( {1 - \sin x} \right)\left( {1 + \sin x} \right))$
$(\frac{{\left( { - 1} \right)\left( {1{\rm{\;}} + {\rm{\;sinx}}} \right)\left( {1 - \sin {\rm{x}}} \right)}}{{\sin {\rm{x\;}} + {\rm{\;}}1}} = \sin {\rm{x}} - 1)$
2. The numerical value of $\frac{5}{sec^{2}\theta}+\frac{2}{1+cot^{2}\theta}+3sin^{2}\theta$ is :
3. What is the value of sin $\frac{-7π}{4}$?
8. What is the value of (1/√3 + cot600)?
9. If 10tanA.tanB = 9, what is the value of cos(A – B)/cos(A + B)?
10. If cot 4A.cot 6A = 1 and A is positive acute angle, then find the value of (12 cos25A – 2) ?