If sin alpha = sin beta and cos alpha = cos b | vedclass

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

Question

(D) Given that $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$. Squaring and adding both equations: $(\sin \alpha)^2 + (\cos \alpha)^2 = (\s

Vedclass · Accepted Answer

$2 n \pi$

Vedclass · Answer

(D) Given that $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$. Squaring and adding both equations: $(\sin \alpha)^2 + (\cos \alpha)^2 = (\sin \beta)^2 + (\cos \beta)^2$ $1 = 1$. Alternatively,consider the complex numbers $z_1 = \cos \alpha + i \sin \alpha$ and $z_2 = \cos \beta + i \sin \beta$. Since $\cos \alpha = \cos \beta$ and $\sin \alpha = \sin \beta$,we have $z_1 = z_2$. This implies $e^{i \alpha} = e^{i \beta}$,which means $e^{i(\alpha - \beta)} = 1$. Therefore,$\alpha - \beta = 2 n \pi$ for some integer $n$. Hence,option $D$ is correct.

If $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$,then $\alpha - \beta = $ for some integer $n$.

Similar Questions

If $A = 130^\circ$ and $x = \sin A + \cos A$,then

If $\sin \theta = \frac{2t}{1+t^2}$ and $\theta$ lies in the second quadrant, then $\cos \theta$ is equal to

If $\cosh 2x = 199$,then $\operatorname{coth} x =$

$\cot 16^{\circ} \cot 44^{\circ} + \cot 44^{\circ} \cot 76^{\circ} - \cot 76^{\circ} \cot 16^{\circ} = $

The value of $\sqrt{3} \cot 20^{\circ} - 4 \cos 20^{\circ}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module