If sin (alpha - beta ) = frac{1}{2} and cos ( | vedclass

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

Question

(A) Given,$\sin (\alpha - \beta ) = \frac{1}{2}$. Since $\sin 30^\circ = \frac{1}{2}$,we have $\alpha - \beta = 30^\circ$ $(i)$.Also,$\cos (\alpha + \

Vedclass · Accepted Answer

$\alpha = 45^\circ, \beta = 15^\circ$

Vedclass · Answer

(A) Given,$\sin (\alpha - \beta ) = \frac{1}{2}$. Since $\sin 30^\circ = \frac{1}{2}$,we have $\alpha - \beta = 30^\circ$ $(i)$.Also,$\cos (\alpha + \beta ) = \frac{1}{2}$. Since $\cos 60^\circ = \frac{1}{2}$,we have $\alpha + \beta = 60^\circ$ $(ii)$.Adding equations $(i)$ and $(ii)$:$(\alpha - \beta ) + (\alpha + \beta ) = 30^\circ + 60^\circ$$2\alpha = 90^\circ \Rightarrow \alpha = 45^\circ$.Substituting $\alpha = 45^\circ$ in equation $(ii)$:$45^\circ + \beta = 60^\circ \Rightarrow \beta = 15^\circ$.Thus,$\alpha = 45^\circ$ and $\beta = 15^\circ$ satisfy both conditions.

If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha$ and $\beta$ are positive acute angles,then

Similar Questions

If $A + B + C = 180^o,$ then the value of $(\cot B + \cot C)(\cot C + \cot A)(\cot A + \cot B)$ is

If $\theta$ and $\phi$ are angles in the $1^{st}$ quadrant such that $\tan \theta = 1/7$ and $\sin \phi = 1/\sqrt{10}$. Then:

$\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}$ is equal to

The value of $\csc \frac{\pi}{18} - \sqrt{3} \sec \frac{\pi}{18}$ is a

The value of $\cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \cdot \dots \cdot \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module