1.
The value of $$\frac{{{\text{co}}{{\text{s}}^2}{{60}^ \circ } + 4{\text{se}}{{\text{c}}^2}{{30}^ \circ } - {\text{ta}}{{\text{n}}^2}{{45}^ \circ }}}{{{{\sin }^2}{{30}^ \circ } + {\text{co}}{{\text{s}}^2}{{30}^ \circ }}}$$      is?

2.
If xsin60°.tan30° - tan45° = cosec60°.cot30° - sec245° then x = ?

3.
If $$\frac{{2{{\tan }^2}{{30}^ \circ }}}{{1 - {{\tan }^2}{{30}^ \circ }}}$$   + $${\sec ^2}{45^ \circ }$$  - $${\sec ^2}{0^ \circ }$$  = $$x\sec {60^ \circ }{\text{,}}$$   then the value of x is?

4.
If xsin60°.tan30° = sec60°.cot45° , then the value of x is?

5.
If tanθ - cotθ = 0 find the value of sinθ + cosθ ?

6.
If α and β are positive acute angles, sin(4α - β) = 1 and cos(2α + β) = $$\frac{1}{2}{\text{,}}$$ then the value of sin(α + 2β) is?

7.
If 0° < A < 90°, then the value of tan2A + cot2A - sec2A cosec2A is?

8.
If $$x{\sin ^2}{60^ \circ }$$  - $$\frac{3}{2}{\text{sec}}{60^ \circ }$$ . $${\text{ta}}{{\text{n}}^2}{30^ \circ }$$  + $$\frac{4}{5}{\sin ^2}{45^ \circ }$$ . $${\text{ta}}{{\text{n}}^2}{60^ \circ }$$  = 0, then x is?

9.
The value of $$\frac{1}{{\sqrt 2 }}{\text{sin}}\frac{\pi }{6}$$ . $${\text{cos}}\frac{\pi }{4}$$ - $$\cot \frac{\pi }{3}$$ . $${\text{sec}}\frac{\pi }{6}$$ + $$\frac{{5\tan \frac{\pi }{4}}}{{12\sin \frac{\pi }{2}}}$$   is equal to?

10.
The numerical value of 1 + $$\frac{1}{{{\text{co}}{{\text{t}}^2}{{63}^ \circ }}}$$  - $${\text{se}}{{\text{c}}^2}{27^ \circ }$$  + $$\frac{1}{{{{\sin }^2}{{63}^ \circ }}}$$  - $${\text{cose}}{{\text{c}}^2}{27^ \circ }$$   is?

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