If cos theta = frac{cos alpha - cos beta}{1 - | vedclass

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

Question

(A) Given,$\cos 	heta = \frac{\cos \alpha - \cos \beta}{1 - \cos \alpha \cos \beta}$.Applying componendo and dividendo,we get:$\frac{1 + \cos 	heta}

Vedclass · Accepted Answer

$\cot \frac{\beta}{2} 	an \frac{\alpha}{2}$

Vedclass · Answer

(A) Given,$\cos 	heta = \frac{\cos \alpha - \cos \beta}{1 - \cos \alpha \cos \beta}$.Applying componendo and dividendo,we get:$\frac{1 + \cos 	heta}{1 - \cos 	heta} = \frac{1 + \frac{\cos \alpha - \cos \beta}{1 - \cos \alpha \cos \beta}}{1 - \frac{\cos \alpha - \cos \beta}{1 - \cos \alpha \cos \beta}}$$\frac{1 + \cos 	heta}{1 - \cos 	heta} = \frac{1 - \cos \alpha \cos \beta + \cos \alpha - \cos \beta}{1 - \cos \alpha \cos \beta - \cos \alpha + \cos \beta}$$\frac{1 + \cos 	heta}{1 - \cos 	heta} = \frac{(1 + \cos \alpha)(1 - \cos \beta)}{(1 - \cos \alpha)(1 + \cos \beta)}$Using half-angle formulas,$\frac{1 + \cos x}{1 - \cos x} = \cot^2 \frac{x}{2}$ and $\frac{1 - \cos x}{1 + \cos x} = 	an^2 \frac{x}{2}$:$\cot^2 \frac{	heta}{2} = \cot^2 \frac{\alpha}{2} 	an^2 \frac{\beta}{2}$Taking the reciprocal on both sides:$	an^2 \frac{	heta}{2} = 	an^2 \frac{\alpha}{2} \cot^2 \frac{\beta}{2}$Taking the square root:$	an \frac{	heta}{2} = 	an \frac{\alpha}{2} \cot \frac{\beta}{2}$

If $\cos \theta = \frac{\cos \alpha - \cos \beta}{1 - \cos \alpha \cos \beta}$,then one of the values of $\tan \frac{\theta}{2}$ is

Similar Questions

The number of points of intersection of the two curves $y = 2\sin x$ and $y = 5x^2 + 2x + 3$ is

If $\tan \theta - \cot \theta = a$ and $\sin \theta + \cos \theta = b,$ then ${({b^2} - 1)^2}({a^2} + 4)$ is equal to

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \}$ and $Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \}$ be two sets. Then

$\frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ} =$

If $\alpha, \beta, \gamma, \delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$,then the value of $4\sin \frac{\alpha}{2} + 3\sin \frac{\beta}{2} + 2\sin \frac{\gamma}{2} + \sin \frac{\delta}{2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module