If \(\tan 6\theta \cdot \tan 3\theta = 1\), where \(0 < \theta < 30^\circ\), then what is \(\theta\) equal to?
10°
\(\tan 6\theta \cdot \tan 3\theta = 1\) means \(\tan 6\theta = \cot 3\theta = \tan(90^\circ-3\theta)\). So \(6\theta = 90^\circ-3\theta\), giving \(9\theta = 90^\circ\), i.e. \(\theta = 10^\circ\), which lies in \(0<\theta<30^\circ\). The correct option is (b).
A rectangle is 48 cm long and 14 cm wide. If the diagonal makes an angle θ with the longer side, then what is (sec θ + cosec θ) equal to?
What is \(\frac{{\sin \theta - \cos \theta + 1}}{{\sin \theta + \cos \theta - 1}} - \frac{{\sin \theta + 1}}{{\cos \theta }}\) equal to?
What is \(\tan \alpha + \tan \beta\) equal to?
What is the ratio of the greatest value of \(\sin^2 x + 2\) (where \(0 \leq x \leq \frac{\pi}{2}\)) to its least value?
If \(cosec~\theta =\frac{29}{21}\) where 0 < θ < 90°, then what is the value of 4 sec θ + 4 tan θ?
The value of \(\cot \left( {cose{c^{ - 1}}\frac{5}{3} + {{\tan }^{ - 1}}\frac{2}{3}\;} \right)\)
The distance of the highest point on the graph of the function y = √3 cos x + sin x from the x-axis is:
If A = π / 6 and B = π / 3, then consider the following statements:
I. sin A + sin B = cos A + cos B
II. tan A + tan B = cot A + cot B
Which of the above statements is / are correct?
If \(\sin A = \frac{1}{{\sqrt 2 }}\) and \({\mathop{\rm Cos}\nolimits} B = \frac{{\sqrt 3 }}{2}\), then, find the value of (A + B)º.
A. 60º
B. 75º
C. 105º
D. 90º