If 1-cot 23^{circ}=frac{x}{1-cot 22^{circ}},t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given,$1-\cot 23^{\circ}=\frac{x}{1-\cot 22^{\circ}}$$x = (1-\cot 23^{\circ})(1-\cot 22^{\circ})$$x = (1 - \frac{\cos 23^{\circ}}{\sin 23^{\circ}}

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given,$1-\cot 23^{\circ}=\frac{x}{1-\cot 22^{\circ}}$$x = (1-\cot 23^{\circ})(1-\cot 22^{\circ})$$x = (1 - \frac{\cos 23^{\circ}}{\sin 23^{\circ}})(1 - \frac{\cos 22^{\circ}}{\sin 22^{\circ}})$$x = \frac{(\sin 23^{\circ} - \cos 23^{\circ})(\sin 22^{\circ} - \cos 22^{\circ})}{\sin 23^{\circ} \sin 22^{\circ}}$$x = \frac{\sin 23^{\circ} \sin 22^{\circ} - \sin 23^{\circ} \cos 22^{\circ} - \cos 23^{\circ} \sin 22^{\circ} + \cos 23^{\circ} \cos 22^{\circ}}{\sin 23^{\circ} \sin 22^{\circ}}$Using $\cos(A-B) = \cos A \cos B + \sin A \sin B$ and $\sin(A+B) = \sin A \cos B + \cos A \sin B$:$x = \frac{\cos(23^{\circ}-22^{\circ}) - \sin(23^{\circ}+22^{\circ})}{\sin 23^{\circ} \sin 22^{\circ}}$$x = \frac{\cos 1^{\circ} - \sin 45^{\circ}}{\sin 23^{\circ} \sin 22^{\circ}}$Using $2 \sin A \sin B = \cos(A-B) - \cos(A+B)$:$x = \frac{2(\cos 1^{\circ} - \sin 45^{\circ})}{\cos(23^{\circ}-22^{\circ}) - \cos(23^{\circ}+22^{\circ})}$$x = \frac{2(\cos 1^{\circ} - \frac{1}{\sqrt{2}})}{\cos 1^{\circ} - \cos 45^{\circ}} = \frac{2(\cos 1^{\circ} - \frac{1}{\sqrt{2}})}{\cos 1^{\circ} - \frac{1}{\sqrt{2}}} = 2$

If $1-\cot 23^{\circ}=\frac{x}{1-\cot 22^{\circ}}$,then $x=$

Similar Questions

$\sum\limits_{r = 1}^{89} {{\log _3}(\tan {r^o})} = $

If $\cos (\theta - \alpha ), \cos \theta$ and $\cos (\theta + \alpha )$ are in $H.P.$,then $\cos \theta \sec \frac{\alpha }{2}$ is equal to

If $\alpha, \beta, \gamma \in \left(0, \frac{\pi}{2}\right)$,then $\frac{\sin(\alpha + \beta + \gamma)}{\sin \alpha + \sin \beta + \sin \gamma}$ is

For any $\theta \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right)$,the expression $3(\sin \theta - \cos \theta)^4 + 6(\sin \theta + \cos \theta)^2 + 4\sin^6 \theta$ equals

Among the following functions defined on $R$ into $R$,the constant function is

Vedclass Test Series

Exam Paper Generator

Online Exam Module