यदि $\tan \theta + \cot \theta = 4$ है,तो $\tan^{4} \theta + \cot^{4} \theta = $

यदि $\tan \alpha = \frac{x^2 - x}{x^2 - x + 1}$ और $\tan \beta = \frac{1}{2x^2 - 2x + 1}$ $(x \ne 0, 1)$,जहाँ $0 < \alpha, \beta < \frac{\pi}{2}$ है,तो $\tan(\alpha + \beta)$ का मान किसके बराबर है?

यदि $(\sec \alpha + \tan \alpha )(\sec \beta + \tan \beta )(\sec \gamma + \tan \gamma ) = \tan \alpha \tan \beta \tan \gamma $ है,तो $(\sec \alpha - \tan \alpha )(\sec \beta - \tan \beta )(\sec \gamma - \tan \gamma ) = $

यदि $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2a$ है,तो $\left(a+\frac{1}{a}\right)$ का मान ज्ञात कीजिए:

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots+\sin 89^{\circ}}{2(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ})+1} = $

$\operatorname{coth}^2 x - \tanh^2 x =$