41. If $$x\cos \theta - y\sin \theta $$ = $$\sqrt {{x^2} + {y^2}} $$ and $$\frac{{{{\cos }^2}\theta }}{{{a^2}}}$$ + $$\frac{{{{\sin }^2}\theta }}{{{b^2}}}$$ = $$\frac{1}{{{x^2} + {y^2}}}{\text{,}}$$ then the correct relation is?
42. If cos2θ - sin2θ = $$\frac{1}{3}{\text{,}}$$ where 0 ≤ θ ≤ $$\frac{\pi }{2}{\text{,}}$$ then the value of cos4θ - sin4θ is?
43. If sinθ + cosθ = $$\sqrt 2 $$ sin(90° - θ) then the value of cotθ is?
44. If $$\frac{{\sin \theta + \cos \theta }}{{\sin \theta - \cos \theta }} = 3{\text{,}}$$ then the value of $${\sin ^4}\theta $$ is?
45. 0 < θ < 90°, tanθ + sinθ =m and tanθ - sinθ = n, where m ≠ n, then the value of m2 - n2 is?
46. If $${\text{0}} < {\text{A}} < {90^ \circ }{\text{,}}$$ then the value of $$\frac{1}{2}\cot {\text{A}}$$ $$\left[ {\frac{{1 + \left( {\operatorname{sec A} - {\text{tan A}}} \right)}}{{\operatorname{cosecA} \left( {\sec {\text{A}} - {\text{tan A}}} \right)}}} \right]$$ = ?
47. The value of following is : $$\frac{{\sin \theta .\operatorname{cosec} \theta .\tan \theta .\cot \theta }}{{{{\sin }^2}\theta + {\text{co}}{{\text{s}}^2}\theta }}$$ ?
48. If cosθ + secθ = $$\sqrt 3 ,$$ then the value of (cos3θ + sec3θ) is?
49. The value of sin22° + sin24° + sin26° + ........ + sin290° is?
50. If $${\text{A}} \times {\text{tan}}\left( {\theta + {{150}^ \circ }} \right)$$ = $${\text{B}} \times \tan $$ $$\left( {\theta - {{60}^ \circ }} \right){\text{,}}$$ the value of $$\frac{{{\text{A}} - {\text{B}}}}{{{\text{A}} + {\text{B}}}}$$ is?
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