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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