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Trigonometric Functions

Multiple Choice Questions

891.

$The minimum value of 27 \tan^{2} (θ) + 3 \cot^{2} (θ) is$

892.

$\cos (36 °) - \cos (72 °) = ?$

1
$\frac{1}{2}$
$\frac{1}{4}$
$\frac{1}{8}$

893.

$If \tan (x) + \tan (x + \frac{π}{3}) + \tan (x + \frac{2 π}{3}) = 3, then \tan (3 x) = ?$

894.

$If 3 \sin (x) + 4 \cos (x) = 5, then 6 \tan (\frac{x}{2}) - 9 \tan^{2} (\frac{x}{2}) = ?$

895.

$If α, β, γ are length of the altitudes of a ∆ ABC with area ∆, then \frac{∆^{2}}{R^{2}} (\frac{1}{α^{2}} + \frac{1}{β^{2}} + \frac{1}{γ^{2}}) = ?$

$\sin^{2} (A) + \sin^{2} (B) + \sin^{2} (C)$
$\cos^{2} (A) + \cos^{2} (B) + \cos^{2} (C)$
$\tan^{2} (A) + \tan^{2} (B) + \tan^{2} (C)$
$\cot^{2} (A) + \cot^{2} (B) + \cot^{2} (C)$

896.

In an acute angled triangle, cot(B)cot(C) + cot(A)cot(C) + cot(A)cot(B) = ?

897.

$x = \log (\frac{1}{y} + \sqrt{1 + \frac{1}{y^{2}}}) \Rightarrow y = ?$

$\tanh (x)$
$\coth (x)$
$sech (x)$
$csch (x)$

898.
The period of f(x) = $\cos (\frac{x}{3}) + \sin (\frac{x}{2})$ is

$2 π$

$4 π$

$8 π$

$12 π$

$12 π$

$Given, f (x) = \cos (\frac{x}{3}) + \sin (\frac{x}{2}) Period of \cos (x) and \sin (x) are 2 π ∴ Period of f (x) = Period of [\cos (\frac{x}{3}) + \sin (\frac{x}{2})] = Period of \cos (\frac{x}{3}) + Period of \sin (\frac{x}{2}) = \frac{2 π}{(\frac{1}{3})} + \frac{2 π}{(\frac{1}{2})} = \frac{6 π}{1} + \frac{4 π}{1} = \frac{LCM of (6 π, 4 π)}{LCM of (1, 1)} = \frac{12 π}{1} = 12 π$