List of top Mathematics Questions on Trigonometric Identities asked in Bihar Board X

If \( \tan(\alpha + \beta) = \sqrt{3} \) and \( \tan \alpha = \frac{1}{\sqrt{3}} \), then the value of \( \tan \beta \) is:
If \( \tan(\alpha + \beta) = \sqrt{3} \) and \( \tan \alpha = \frac{1}{\sqrt{3}} \), then the value of \( \tan \beta \) is
If \( \sin \theta = \frac{\sqrt{3}}{2} \), \( 0^\circ<\theta<90^\circ \), then \( \tan^2 \theta - 1 = \) ?
Evaluate \( 9 \csc^2 22^\circ - 9 \cot^2 22^\circ + 1 = \):
If \( \tan 2A = \cot(A - 18^\circ) \), where \( 2A \) is an acute angle, then the value of \( A \) is:
If \( \sin \theta = \frac{a}{b} \), then the value of \( \cos \theta \) is:
If \( \sec \theta = \frac{13}{12} \), then \( \cot \theta = \):
sec\(^2 23^\circ\) - tan\(^2 23^\circ\) + 2 =
If \( x \cos \theta = 1 \) and \( \tan \theta = y \), then the value of \( x^2 - y^2 \) is
If \( \tan \theta = \frac{3}{4} \), then \( \sin \theta \) is
tan 5° · tan 25° · tan 30° · tan 65° · tan 85° =
cos 38° · cos 52° - sin 38° · sin 52° =
\[ \frac{\text{cosec} 42^\circ}{\sec 48^\circ} \times \frac{\cos 37^\circ}{\sin 53^\circ} = \]
\( \sqrt{2} \left( \sin \frac{\pi}{4} + \cos \frac{\pi}{4} \right) =\)
If \( a \cos \theta + b \sin \theta = 4 \) and \( a \sin \theta - b \cos \theta = 3 \), then the value of \( a^2 + b^2 \) is
If \( \tan 2A = \cot (A - 18^\circ) \) where \( 2A \) is an acute angle, then the value of \( A \) is:
If \( \sin \theta = \frac{a}{b} \), then the value of \( \cos \theta \) is:
Prove that:
\[ \frac{\sec^3 0}{\sec^2 0 -1} + \frac{\cosec^3 0}{\cosec^2 0 -1} = \sec 0 \cosec 0 ( \sec 0 + \cosec 0 ). \]
Find the value of \( 4\tan^2 45^\circ + \cos^2 30^\circ - \sin^2 60^\circ \).
Evaluate: \( \csc 39^\circ \cos 51^\circ + \tan 21^\circ \cot 69^\circ - \sec^2 21^\circ \)
Prove that \( \sec^4 \theta - \tan^4 \theta = 1 + 2\tan^2 \theta \).
\( \tan 5^\circ \cdot \tan 25^\circ \cdot \tan 30^\circ \cdot \tan 65^\circ \cdot \tan 85^\circ \) is:
\( \cos 38^\circ \cos 52^\circ - \sin 38^\circ \sin 52^\circ \) is:
\( \frac{\csc 42^\circ \cdot \cos 37^\circ}{\sec 48^\circ \cdot \sin 53^\circ} \) is:
\( \sqrt{2} \left(\sin \frac{\pi}{4} + \cos \frac{\pi}{4} \right) \) is: