41. What is the value of $$\frac{{{{\left[ {1 - \tan \left( {{{90}^ \circ } - \theta } \right)} \right]}^2}}}{{\left[ {{{\cos }^2}\left( {{{90}^ \circ } - \theta } \right)} \right]}} - 1 = ?$$
42. What is the value of cos15° - cos165°?
43. If 4 - 2sin2θ - 5cosθ = 0, 0° < θ < 90°, then the value of sinθ + tanθ is:
44. The value of $$\left( {\frac{{\sin A}}{{1 - \cos A}} + \frac{{1 - \cos A}}{{\sin A}}} \right) \div \left( {\frac{{{{\cot }^2}A}}{{1 + {\text{cosec}}\,A}} + 1} \right){\text{is:}}$$
45. Evaluate the following expression in terms of trigonometric ratios.
$$\frac{{{{\cot }^2}A\left( {\sec A - 1} \right)}}{{1 + \sin A}}$$
$$\frac{{{{\cot }^2}A\left( {\sec A - 1} \right)}}{{1 + \sin A}}$$
46. If $$\frac{{{{\sin }^2}\theta - 3\sin \theta + 2}}{{{{\cos }^2}\theta }} = 1,$$ where 0° < θ < 90°, then what is the value of (cos2θ + sin3θ + cosec2θ)?
47. The value of $$\sqrt {{{\sec }^2}\theta + {\text{cose}}{{\text{c}}^2}\theta } \times \sqrt {{{\tan }^2}\theta - {{\sin }^2}\theta } $$ is equal to:
48. If tanθ + secθ = 7, θ being acute, then the value of 5sinθ is:
49. Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$
50. If sec2θ + tan2θ = $$3\frac{1}{2},$$ 0° < θ < 90°, then (cosθ + sinθ) is equal to
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