51. If sinα .sec(30° + α) = 1, (0 < α < 60°), then the value of sinα + cos2α is?
52. If ∠A and ∠B are complementary to each other, then the value of sec2A + sec2B - sec2A.sec2B is?
53. The value of cotθ.tan(90° - θ) - sec(90° - θ)cosecθ + (sin225° + sin265°) + $$\sqrt 3 $$ (tan5°. tan15°. tan30°. tan75°. tan85°)
54. If cosθ.cosec23° = 1, the value of θ is?
55. If A, B and C be the angles of a triangle, the incorrect relation is ?
56. If $$\theta $$ is a positive acute angle and $$\tan 2\theta .\tan 3\theta $$ = 1 then the value of $$\left( {{\text{2co}}{{\text{s}}^2}\frac{{5\theta }}{2} - 1} \right)$$ is?
57. If tan7θ.tan2θ = 1, then the value of tan3θ is?
58. If $${\text{sin}}\left( {{{60}^ \circ } - \theta } \right)$$ = $${\text{cos}}\left( {\psi - {{30}^ \circ }} \right),$$ then the value of $${\text{tan}}\left( {\psi - \theta } \right)$$ is (assume that $$\theta $$ and $$\psi $$ are both positive acute angles with$$\theta < {60^ \circ }$$ and $$\psi > {30^ \circ }$$ ) ?
59. Evaluate : 3cos80°.cosec10° + 2cos59°.cosec31°
60. $$\frac{{2{\text{sin }}{{68}^ \circ }}}{{{\text{cos 2}}{{\text{2}}^ \circ }}}$$ $$ - $$ $$\frac{{2{\text{cot 1}}{5^ \circ }}}{{5\tan {{75}^ \circ }}}$$ $$ - $$ $$\frac{{3\tan {{45}^ \circ }.\tan {{20}^ \circ }.\tan {{40}^ \circ }.\tan {{50}^ \circ }.\tan {{70}^ \circ }}}{5}$$ is equal to?
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