Class 10 Maths – Introduction to Trigonometry Quiz

If \(\sin \theta = 1\), then the value of \(\frac{1}{2}\sin\frac{\theta}{2}\) is:

Evaluate: \(\frac{5\cos^2 60^\circ + 4\sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \sin^2 60^\circ}\)

\(\frac{\cos^2 \theta}{\sin^2 \theta} - \frac{1}{\sin^2 \theta}\), in simplified form, is:

If \(\theta\) is an acute angle of a right-angled triangle, then which of the following equations is not true?

\((\cos^4 A - \sin^4 A)\), on simplification, gives:

If \(\tan \theta = \frac{x}{y}\), then \(\cos \theta\) is equal to:

\(\sec \theta\), when expressed in terms of \(\cot \theta\), is equal to:

Which of the following is true for all values of \(\theta\), where \(0^{\circ} < \theta < 90^{\circ}\)?

\((\sec^2 \theta - 1)(\mathrm{cosec}^2 \theta - 1)\) is equal to:

If \(\sin \theta - \cos \theta = 0\) and \(\theta\) is acute, then the value of \(\sin^4 \theta + \cos^4 \theta\) is:

If \(\cot \theta = \frac{1}{\sqrt{3}}\), then the value of \(\sec^2 \theta + \mathrm{cosec}^2 \theta\) is:

Given that \(\sec \theta = \sqrt{2}\), the value of \(\frac{1 + \tan \theta}{\sin \theta}\) is:

If \(\theta\) is an acute angle and \(\tan \theta + \cot \theta = 2\), then the value of \(\sin^3 \theta + \cos^3 \theta\) is:

If \(a \cot \theta + b\, \mathrm{cosec}\, \theta = p\) and \(b \cot \theta + a\, \mathrm{cosec}\, \theta = q\), then \(p^2 - q^2\) is equal to:

If \(\sec \theta + \tan \theta = p\), then the value of \(\tan \theta\) is:

The value of \((1 + \tan^2 \theta)(1 - \sin \theta)(1 + \sin \theta)\) is:

In a right-angled triangle \(ABC\), right-angled at \(C\), if \(\sin A = \frac{3}{5}\), then the value of \(\tan A\) is:

The value of \(2 \tan 45^\circ \cdot \cos 60^\circ\) is:

If \(\sec \theta = \sqrt{2}\) and \(\theta\) is acute, then the value of \(\tan^2 \theta + \sin^2 \theta\) is:

If \(\sin \theta + \cos \theta = \sqrt{2}\), then the value of \(\tan \theta + \cot \theta\) is: