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Trigonometric Functions

Multiple Choice Questions

771.
A man is standing on the horizontal plane. The angle of elevation of top of the pole is $α$ . If he walks a distance double the height of the pole, then the elevation of the pole is $2 α$ . The value of $α$ is

$\frac{π}{12}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{6}$

$\frac{π}{12}$

Let the height of the pole be BC = h m.

$In ∆ ABC, \tan (2 α) = \frac{h}{x} . . . (i)$

$and in ∆ DBC, \tan (α) = \frac{h}{2 h + x} \Rightarrow \tan (α) = \frac{\frac{h}{x}}{2 (\frac{h}{x}) + 1} \Rightarrow \tan (α) = \frac{\tan (2 α)}{2 \tan (2 α) + 1} \Rightarrow \tan (α) (2 \tan (2 α + 1)) = \tan (2 α) \Rightarrow \tan (α) [2 \times \frac{2 \tan (α)}{1 - \tan^{2} (α)}] = \frac{2 \tan (α)}{1 - \tan^{2} (α)} \Rightarrow [4 \tan (α) + 1 - \tan^{2} (α)] = 2 \Rightarrow \tan^{2} (α) - 4 \tan (α) + 1 = 0 \Rightarrow \tan (α) = \frac{+ 4 \pm \sqrt{16 - 4}}{2 \times 1} = \frac{4 \pm \sqrt{12}}{2} = \frac{4 \pm 2 \sqrt{3}}{2} \Rightarrow \tan (α) = 2 \pm \sqrt{3}$

$Taking' -' sign, we get \Rightarrow \tan (α) = 2 - \sqrt{3} \Rightarrow \tan (α) = \tan (15 °) \Rightarrow α = 15 ° or \frac{π}{12}$

772.

The value of sin(50°) cos (10°) + cos(50°) sin(10°) is

$\frac{1}{2}$
$\sqrt{3}$
$\frac{\sqrt{3}}{2}$
1

773.

The least value of a, for which the function a $\frac{4}{\sin (x)} + \frac{1}{1 - \sin (x)}$ has at east one solution in the interval $(0, \frac{π}{2})$ , is

774.

In $∆ ABC$ , if 3a = b + c, then value of $\cot (\frac{B}{2}) \cot (\frac{C}{2})$ will be

1
2
$\sqrt{3}$
$\sqrt{2}$

775.

If sin(a) and cos(a) are the roots of the equation ax² + bx + c = 0, then

a² - b² + 2ac = 0
(a - c)² = b² + c²
a² + b² - 2ac = 0
a² + b² + 2ac = 0

776.

In $∆ ABC$ , if cot(A), cot(B) and cot(C) are in AP, then a², b² and c² are in

HP
AP
GP
None of the above

777.

The maximum value of $3 \cos (θ) + 4 \sin (θ)$ is

3
4
5
None of these

778.

The period of $\sin (θ) - \sqrt{3} \cos (θ)$ is

$\frac{π}{4}$
$\frac{π}{2}$
$π$
$2 π$

779.

If $\cos (θ) = \frac{\cos^{2} (α) + \cos^{2} (β) + \cos^{2} (γ)}{\sin^{2} (α) + \sin^{2} (β) + \sin (γ)}$ , where $α, β, γ$ are the angles made by a line with the positive directions of the axes of reference, then the measure of $θ$ is