If \(\sin\theta + \csc\theta = 2\), then \(\sin^2\theta + \csc^2\theta\) is equal to
1
4
2
None of these
If \(f(x)=\cos^2 x + \sec^2 x\), then
\(f(x) < 1\)
\(f(x)=1\)
\(2 < f(x) < 1\)
\(f(x) \ge 2\)
If \(\tan\theta=\dfrac{1}{2}\) and \(\tan\phi=\dfrac{1}{3}\), then the value of \(\theta+\phi\) is
\(\dfrac{\pi}{6}\)
\(\pi\)
0
\(\dfrac{\pi}{4}\)
Which of the following is not correct?
\(\sin\theta = -\dfrac{1}{5}\)
\(\cos\theta = 1\)
\(\sec\theta = \dfrac{1}{2}\)
\(\tan\theta = 20\)
The value of \(\tan1^\circ\tan2^\circ\tan3^\circ\dots\tan89^\circ\) is
0
1
\(\dfrac{1}{2}\)
Not defined
The value of \(\dfrac{1-\tan^2 15^\circ}{1+\tan^2 15^\circ}\) is
1
\(\sqrt{3}\)
\(\dfrac{\sqrt{3}}{2}\)
2
The value of \(\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\) is
\(\dfrac{1}{\sqrt{2}}\)
0
1
-1
If \(\tan\theta=3\) and \(\theta\) lies in the third quadrant, then the value of \(\sin\theta\) is
\(\dfrac{1}{\sqrt{10}}\)
\(-\dfrac{1}{\sqrt{10}}\)
\(-\dfrac{3}{\sqrt{10}}\)
\(\dfrac{3}{\sqrt{10}}\)
The value of \(\tan75^\circ - \cot75^\circ\) is equal to
\(2\sqrt{3}\)
2 + \(\sqrt{3}\)
2 - \(\sqrt{3}\)
1
Which of the following is correct?
\(\sin1^\circ > \sin1\)
\(\sin1^\circ < \sin1\)
\(\sin1^\circ = \sin1\)
\(\sin1^\circ = \dfrac{\pi}{18}\sin1\)
If \(\tan\alpha=\dfrac{m}{m+1}\), \(\tan\beta=\dfrac{1}{2m+1}\), then \(\alpha+\beta\) is equal to
\(\dfrac{\pi}{2}\)
\(\dfrac{\pi}{3}\)
\(\dfrac{\pi}{6}\)
\(\dfrac{\pi}{4}\)
The minimum value of \(3\cos x + 4\sin x + 8\) is
5
9
7
3
The value of \(\tan3A - \tan2A - \tan A\) is equal to
\(\tan3A\tan2A\tan A\)
\(-\tan3A\tan2A\tan A\)
\(\tan A\tan2A - \tan2A\tan3A - \tan3A\tan A\)
None of these
The value of \(\sin(45^\circ + \theta) - \cos(45^\circ - \theta)\) is
\(2\cos\theta\)
\(2\sin\theta\)
1
0
The value of \(\cot\left(\dfrac{\pi}{4}+\theta\right)\cot\left(\dfrac{\pi}{4}-\theta\right)\) is
-1
0
1
Not defined
\(\cos2\theta\cos2\phi + \sin^2(\theta-\phi) - \sin^2(\theta+\phi)\) is equal to
\(\sin2(\theta+\phi)\)
\(\cos2(\theta+\phi)\)
\(\sin2(\theta-\phi)\)
\(\cos2(\theta-\phi)\)
The value of \(\cos12^\circ + \cos84^\circ + \cos156^\circ + \cos132^\circ\) is
\(\dfrac{1}{2}\)
1
\(-\dfrac{1}{2}\)
\(\dfrac{1}{8}\)
If \(\tan A=\dfrac{1}{2}\), \(\tan B=\dfrac{1}{3}\), then \(\tan(2A+B)\) is equal to
1
2
3
4
The value of \(\sin\dfrac{\pi}{10} - \sin\dfrac{13\pi}{10}\) is
\(\dfrac{1}{2}\)
\(-\dfrac{1}{2}\)
\(-\dfrac{1}{4}\)
1
The value of \(\sin50^\circ - \sin70^\circ + \sin10^\circ\) is equal to
1
0
\(\dfrac{1}{2}\)
2
If \(\sin\theta + \cos\theta = 1\), then the value of \(\sin2\theta\) is equal to
1
\(\dfrac{1}{2}\)
0
-1
If \(\alpha + \beta = \dfrac{\pi}{4}\), then the value of \((1+\tan\alpha)(1+\tan\beta)\) is
1
2
-2
Not defined
If \(\sin\theta = -\dfrac{4}{5}\) and \(\theta\) lies in the third quadrant, then the value of \(\cos\dfrac{\theta}{2}\) is
\(\dfrac{1}{5}\)
-\(\dfrac{1}{\sqrt{10}}\)
-\(\dfrac{1}{\sqrt{5}}\)
\(\dfrac{1}{\sqrt{10}}\)
Number of solutions of the equation \(\tan x + \sec x = 2\cos x\) lying in the interval \([0,2\pi]\) is
0
1
2
3
The value of \(\sin\dfrac{\pi}{18} + \sin\dfrac{\pi}{9} + \sin\dfrac{2\pi}{9} + \sin\dfrac{5\pi}{18}\) is given by
\(\sin\dfrac{7\pi}{18} + \sin\dfrac{4\pi}{9}\)
1
\(\cos\dfrac{\pi}{6} + \cos\dfrac{3\pi}{7}\)
\(\cos\dfrac{\pi}{9} + \sin\dfrac{\pi}{9}\)
If \(A\) lies in the second quadrant and \(3\tan A + 4 = 0\), then the value of \(2\cot A - 5\cos A + \sin A\) is equal to
-\(\dfrac{53}{10}\)
\(\dfrac{23}{10}\)
\(\dfrac{37}{10}\)
\(\dfrac{7}{10}\)
The value of \(\cos^2 48^\circ - \sin^2 12^\circ\) is
\(\dfrac{\sqrt{5}+1}{8}\)
\(\dfrac{\sqrt{5}-1}{8}\)
\(\dfrac{\sqrt{5}+1}{5}\)
\(\dfrac{\sqrt{5}+1}{2\sqrt{2}}\)
If \(\tan\alpha=\dfrac{1}{7}\), \(\tan\beta=\dfrac{1}{3}\), then \(\cos2\alpha\) is equal to
\(\sin2\beta\)
\(\sin4\beta\)
\(\sin3\beta\)
\(\cos2\beta\)
If \(\tan\theta=\dfrac{a}{b}\), then \(b\cos2\theta + a\sin2\theta\) is equal to
a
b
\(\dfrac{a}{b}\)
None
If for real values of \(x\), \(\cos\theta = x + \dfrac{1}{x}\), then
\(\theta\) is an acute angle
\(\theta\) is right angle
\(\theta\) is an obtuse angle
No value of \(\theta\) is possible