Trigonometry MCQs

Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$

If $$\cos \pi x = {x^2} - x + \frac{5}{4}{\text{,}}$$     then the value of x will be ?

sin⁴θ + cos⁴θ in terms of sinθ can be written as:

In a ΔABC, if 4∠A = 3∠B = 12∠C, find ∠A?

If 3tanθ = 2√3sin, 0° < θ < 90°, then the value of $$\frac{{{\text{cose}}{{\text{c}}^2}2\theta + {{\cot }^2}2\theta }}{{{{\sin }^2}\theta + {{\tan }^2}\theta }}$$    is:

$$\frac{{2{\text{sin }}{{68}^ \circ }}}{{{\text{cos 2}}{{\text{2}}^ \circ }}}$$   $$ - $$ $$\frac{{2{\text{cot 1}}{5^ \circ }}}{{5\tan {{75}^ \circ }}}$$   $$ - $$ $$\frac{{3\tan {{45}^ \circ }.\tan {{20}^ \circ }.\tan {{40}^ \circ }.\tan {{50}^ \circ }.\tan {{70}^ \circ }}}{5}$$         is equal to?

If 1 + cos²θ = 3sinθ cosθ, then the integral value of cotθ is $$\left( {0 < \theta < \frac{\pi }{2}} \right) = \,?$$

If x, y are acute angles, 0 < x + y < 90° and sin(2x - 20°) = cos(2y + 20°), then the value of tan(x + y) is?

If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is?