The value of frac{sin 55^{circ} - cos 55^{cir | vedclass

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

Question

(D) We know that $\cos 55^{\circ} = \sin(90^{\circ} - 55^{\circ}) = \sin 35^{\circ}$.Substituting this into the expression, we get $\frac{\sin 55^{\ci

Vedclass · Accepted Answer

$\sqrt{2}$

Vedclass · Answer

(D) We know that $\cos 55^{\circ} = \sin(90^{\circ} - 55^{\circ}) = \sin 35^{\circ}$.Substituting this into the expression, we get $\frac{\sin 55^{\circ} - \sin 35^{\circ}}{\sin 10^{\circ}}$.Using the formula $\sin C - \sin D = 2 \cos\left(\frac{C+D}{2}ight) \sin\left(\frac{C-D}{2}ight)$, we have:$\sin 55^{\circ} - \sin 35^{\circ} = 2 \cos\left(\frac{55^{\circ} + 35^{\circ}}{2}ight) \sin\left(\frac{55^{\circ} - 35^{\circ}}{2}ight) = 2 \cos 45^{\circ} \sin 10^{\circ}$.Now, the expression becomes $\frac{2 \cos 45^{\circ} \sin 10^{\circ}}{\sin 10^{\circ}} = 2 \cos 45^{\circ}$.Since $\cos 45^{\circ} = \frac{1}{\sqrt{2}}$, the value is $2 	imes \frac{1}{\sqrt{2}} = \sqrt{2}$.

The value of $\frac{\sin 55^{\circ} - \cos 55^{\circ}}{\sin 10^{\circ}}$ is

Similar Questions

Which of the following is correct?

If $\tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha}$,then $\sin \alpha + \cos \alpha$ and $\sin \alpha - \cos \alpha$ are equal to:

If $\tan \theta = \frac{20}{21}$,then $\cos \theta$ will be

If $y = \log_e \tan \left(\frac{\pi}{4} + \frac{x}{2}\right)$,then $\tanh \left(\frac{y}{2}\right) = $

The value of $(\sin 210^{\circ})(\sin 585^{\circ})$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module