If theta = 3alpha and sin theta = frac{a}{sqr | vedclass

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

Question

(A) Given $	heta = 3\alpha$ and $\sin 3\alpha = \frac{a}{\sqrt{a^2 + b^2}}$.Let $\cos 3\alpha = \frac{b}{\sqrt{a^2 + b^2}}$.We need to evaluate $E =

Vedclass · Accepted Answer

$2\sqrt{a^2 + b^2}$

Vedclass · Answer

(A) Given $	heta = 3\alpha$ and $\sin 3\alpha = \frac{a}{\sqrt{a^2 + b^2}}$.Let $\cos 3\alpha = \frac{b}{\sqrt{a^2 + b^2}}$.We need to evaluate $E = a \csc \alpha - b \sec \alpha = \frac{a}{\sin \alpha} - \frac{b}{\cos \alpha} = \frac{a \cos \alpha - b \sin \alpha}{\sin \alpha \cos \alpha}$.Substitute $a = \sqrt{a^2 + b^2} \sin 3\alpha$ and $b = \sqrt{a^2 + b^2} \cos 3\alpha$:$E = \frac{\sqrt{a^2 + b^2} (\sin 3\alpha \cos \alpha - \cos 3\alpha \sin \alpha)}{\sin \alpha \cos \alpha}$.Using the identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$:$E = \frac{\sqrt{a^2 + b^2} \sin(3\alpha - \alpha)}{\sin \alpha \cos \alpha} = \frac{\sqrt{a^2 + b^2} \sin 2\alpha}{\sin \alpha \cos \alpha}$.Since $\sin 2\alpha = 2 \sin \alpha \cos \alpha$:$E = \frac{\sqrt{a^2 + b^2} (2 \sin \alpha \cos \alpha)}{\sin \alpha \cos \alpha} = 2\sqrt{a^2 + b^2}$.

If $\theta = 3\alpha$ and $\sin \theta = \frac{a}{\sqrt{a^2 + b^2}}$,then the value of the expression $a \csc \alpha - b \sec \alpha$ is:

Similar Questions

If $\frac{\tan 3A}{\tan A} = a$,then $\frac{\sin 3A}{\sin A}$ is equal to

If $\tan \alpha = \frac{-12}{5}$,$\cot \beta = \frac{7}{24}$,$\alpha$ does not belong to the second quadrant,and $\beta$ does not belong to the first quadrant,then $\sqrt{13} \sin \frac{\alpha}{2} + \cos \frac{\beta}{2} + \tan \frac{\alpha}{2} \cot \frac{\beta}{2} = $

If $\csc \theta = \frac{p + q}{p - q}$ $(p \neq q \neq 0)$,then $\left| \cot \left( \frac{\pi}{4} + \frac{\theta}{2} \right) \right|$ is equal to

If $\tan A = \frac{1 - \cos B}{\sin B},$ find $\tan 2A$ in terms of $\tan B$.

$\frac{\sin 5 \theta}{\sin \theta}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module