If cos (theta+phi)=frac{3}{5} and sin (theta- | vedclass

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

Question

(A) Given $\cos (	heta+\phi) = \frac{3}{5}$, since $0 < 	heta, \phi < \frac{\pi}{4}$, we have $	an (	heta+\phi) = \frac{4}{3}$.Given $\sin (	heta

Vedclass · Accepted Answer

$\frac{16}{63}$

Vedclass · Answer

(A) Given $\cos (	heta+\phi) = \frac{3}{5}$, since $0 Given $\sin (	heta-\phi) = \frac{5}{13}$, we have $	an (	heta-\phi) = \frac{5}{12}$.We know that $2	heta = (	heta+\phi) + (	heta-\phi)$.Therefore, $	an (2	heta) = 	an ((	heta+\phi) + (	heta-\phi)) = \frac{	an (	heta+\phi) + 	an (	heta-\phi)}{1 - 	an (	heta+\phi) 	an (	heta-\phi)}$.Substituting the values: $	an (2	heta) = \frac{\frac{4}{3} + \frac{5}{12}}{1 - (\frac{4}{3} 	imes \frac{5}{12})} = \frac{\frac{16+5}{12}}{1 - \frac{20}{36}} = \frac{\frac{21}{12}}{\frac{16}{36}} = \frac{21}{12} 	imes \frac{36}{16} = \frac{21 	imes 3}{16} = \frac{63}{16}$.Thus, $\cot (2	heta) = \frac{1}{	an (2	heta)} = \frac{16}{63}$.

If $\cos (\theta+\phi)=\frac{3}{5}$ and $\sin (\theta-\phi)=\frac{5}{13}$, where $0 < \theta, \phi < \frac{\pi}{4}$, then $\cot (2 \theta)$ has the value:

Similar Questions

If $\alpha+\beta=\gamma$,then what is the value of $\cos^2 \alpha+\cos^2 \beta+\cos^2 \gamma$ equal to?

$\cos 66^{\circ} + \sin 84^{\circ} = $

If $\sin x = \frac{3}{5}$ and $\cos y = -\frac{12}{13}$,where $x$ and $y$ both lie in the second quadrant,find the value of $\sin (x+y)$.

If $(1 + \tan \theta )(1 + \tan \phi ) = 2$,then $\theta + \phi = \dots ^\circ$

If $A = \frac{\pi}{24}$,then $\frac{\cos A + \cos 3A + \cos 5A + \cos 7A}{\sin A + \sin 3A + \sin 5A + \sin 7A} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module