31. The value of tan2θ + cot2θ - sec2θcosec2θ is equal to:
32. If 1 + 2tan2θ + 2sinθsec2θ = $$\frac{a}{b}$$, 0° < θ < 90°, then $$\frac{{a + b}}{{a - b}}?$$
33. If sinθ = 4cosθ, then what is the value of sinθcosθ?
34. What is the value of $$\frac{{2\left( {1 - {{\sin }^2}\theta } \right){\text{cose}}{{\text{c}}^2}\theta }}{{{{\cot }^2}\theta \left( {1 + {{\tan }^2}\theta } \right)}} - 1$$
35. What is the value of $$\frac{{{{\left[ {\tan \left( {{{90}^ \circ } - A} \right) + \cot \left( {{{90}^ \circ } - A} \right)} \right]}^2}}}{{\left[ {2{{\sec }^2}\left( {{{90}^ \circ } - 2A} \right)} \right]}}?$$
36. $${\left( {\frac{{\sin \theta - 2{{\sin }^3}\theta }}{{2{{\cos }^3} - \cos \theta }}} \right)^2} + 1,$$ θ ≠ 45° is equal to:
37. If $$\frac{{1 + \sin \theta }}{{1 - \sin \theta }} = \frac{{{p^2}}}{{{q^2}}},$$ then secθ is equal to:
38. What is the value of $$\frac{{\left[ {\sin \left( {90 - A} \right) + \cos \left( {180 - 2A} \right)} \right]}}{{\left[ {\cos \left( {90 - 2A} \right) + \sin \left( {180 - A} \right)} \right]}}?$$
39. If cos53° = $$\frac{x}{y},$$ then sec53° + cot37° is equal to:
40. $$\frac{{\sin \theta - \cos \theta + 1}}{{\sin \theta + \cos \theta - 1}} = ?$$
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