1. 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?
2. 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?
3. 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?
4. If 0° < A < 90°, then the value of tan2A + cot2A - sec2A cosec2A is?
5. 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?
6. If θ is a positive acute angle and 4cos2θ - 1 = 0, then the value of tan(θ - 15°) is equal to?
7. The value of $$\frac{{\sin {{25}^ \circ }.\cos {{65}^ \circ } + \cos {{25}^ \circ }.\sin {{65}^ \circ }}}{{{{\tan }^2}{{70}^ \circ } - {\text{cose}}{{\text{c}}^2}{{20}^ \circ }}}$$ is?
8. If $$\theta + \phi = \frac{\pi }{2}$$ and $$\sin \theta = \frac{1}{2},$$ then the value of $${\text{sin}}\phi $$ is?
9. Find the value of the following 3(sin4θ + cos4θ) + 2(sin6θ + cos6θ) + 12sin2θ.cos2θ = ?
10. The numerical value of $$\frac{{{\text{co}}{{\text{s}}^2}{{45}^ \circ }}}{{{{\sin }^2}{{60}^ \circ }}}$$ + $$\frac{{{\text{co}}{{\text{s}}^2}{{60}^ \circ }}}{{{{\sin }^2}{{45}^ \circ }}}$$ - $$\frac{{{\text{ta}}{{\text{n}}^2}{{30}^ \circ }}}{{{\text{co}}{{\text{t}}^2}{{45}^ \circ }}}$$ - $$\frac{{{{\sin }^2}{{30}^ \circ }}}{{{\text{co}}{{\text{t}}^2}{{30}^ \circ }}}$$ is?
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