If tan A = n tan B and sin A = m sin B , then | vedclass

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

Question

(A) Given: $	an A = n 	an B$ and $\sin A = m \sin B$.From the first equation: $\frac{\sin A}{\cos A} = n \frac{\sin B}{\cos B} \Rightarrow \frac{\si

Vedclass · Accepted Answer

$\frac{m^{2}-1}{n^{2}-1}$

Vedclass · Answer

(A) Given: $	an A = n 	an B$ and $\sin A = m \sin B$.From the first equation: $\frac{\sin A}{\cos A} = n \frac{\sin B}{\cos B} \Rightarrow \frac{\sin A}{\sin B} = n \frac{\cos A}{\cos B}$.Since $\sin A = m \sin B$,we have $\frac{\sin A}{\sin B} = m$.Equating the two expressions for $\frac{\sin A}{\sin B}$,we get $m = n \frac{\cos A}{\cos B}$,which implies $\cos B = \frac{n}{m} \cos A$.Also,from $\sin A = m \sin B$,we get $\sin B = \frac{1}{m} \sin A$.Using the identity $\sin^2 B + \cos^2 B = 1$:$(\frac{1}{m} \sin A)^2 + (\frac{n}{m} \cos A)^2 = 1$.$\frac{1}{m^2} \sin^2 A + \frac{n^2}{m^2} \cos^2 A = 1$.$\sin^2 A + n^2 \cos^2 A = m^2$.Substituting $\sin^2 A = 1 - \cos^2 A$:$(1 - \cos^2 A) + n^2 \cos^2 A = m^2$.$(n^2 - 1) \cos^2 A = m^2 - 1$.Therefore,$\cos^2 A = \frac{m^2 - 1}{n^2 - 1}$.

If $\tan A = n \tan B$ and $\sin A = m \sin B ,$ then the value of $\cos ^{2} A$ is

Similar Questions

The simplest value of $\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \tan 89^{\circ}$ is

If $\sin A = \frac{1}{\sqrt{10}}$ and $\sin B = \frac{1}{\sqrt{5}}$,where $A$ and $B$ are positive acute angles,then $A + B = $

The value of $\frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$ is equal to:

If $\sec \alpha + \tan \alpha = 2,$ then the value of $\sin \alpha$ is (assume that $0 < \alpha < 90^{\circ}$).

The maximum value of $\cos \alpha_1 \cdot \cos \alpha_2 \cdots \cos \alpha_n$ under the restrictions $0 \le \alpha_1, \alpha_2, \dots, \alpha_n \le \frac{\pi}{2}$ and $\cot \alpha_1 \cdot \cot \alpha_2 \cdots \cot \alpha_n = 1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module