51. If 12cot2θ - 31cosecθ + 32 = 0, 0° < θ < 90° then the value of tanθ will be:
52. The expression $$\frac{{{{\cos }^4}\theta - {{\sin }^4}\theta + 2{{\sin }^2}\theta + 3}}{{\left( {{\text{cosec}}\,\theta + \cot \theta + 1} \right)\left( {{\text{cosec}}\,\theta - \cot \theta + 1} \right) - 2}},$$ is equal to:
53. If sin(A + B) = $$\frac{{\sqrt 3 }}{2}$$ and tan(A - B) = $$\frac{1}{{\sqrt 3 }}$$ , then (2A + 3B) is equal to.
54. If sinθ = $$\frac{9}{{41}},$$ 0° < θ < 90° then what is the value of cotθ?
55. What will be the value of sin10° - $$\frac{4}{3}$$sin310°?
56. Evaluate the following expression in terms of trigonometric ratios. $$\frac{{\sec A - \tan A}}{{\sec A + \tan A}}$$
57. If A = 10°, what is the value of: $$\frac{{12\sin 3A + 5\cos \left( {5A - {5^ \circ }} \right)}}{{9\sin \frac{{9A}}{2} - 4\cos \left( {5A + {{10}^ \circ }} \right)}}?$$
58. $$\sqrt {\frac{{\cot \theta + \cos \theta }}{{\cot \theta - \cos \theta }}} $$ is equal to-
59. Simplify: cos(36° - A)cos(36° + A) + cos(54° - A)cos(54° + A)
60. If 3(cot2θ - cos2θ) = cos2θ, 0°< θ < 90°, then the value of (tan2θ + cosec2θ + sin2θ) is:
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