જો theta = 3alpha અને sin theta = frac{a}{sqr | vedclass

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

Question

(B) આપેલ પદાવલિ: $E = a \operatorname{cosec} \alpha - b \sec \alpha = \frac{a}{\sin \alpha} - \frac{b}{\cos \alpha}$.$E = \frac{a \cos \alpha - b \sin

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) આપેલ પદાવલિ: $E = a \operatorname{cosec} \alpha - b \sec \alpha = \frac{a}{\sin \alpha} - \frac{b}{\cos \alpha}$.$E = \frac{a \cos \alpha - b \sin \alpha}{\sin \alpha \cos \alpha}$.$\sqrt{a^2 + b^2}$ વડે ગુણતા અને ભાગતા:$E = \frac{\sqrt{a^2 + b^2}}{\sin \alpha \cos \alpha} \left( \frac{a}{\sqrt{a^2 + b^2}} \cos \alpha - \frac{b}{\sqrt{a^2 + b^2}} \sin \alpha ight)$.$\sin 	heta = \sin 3\alpha = \frac{a}{\sqrt{a^2 + b^2}}$ હોવાથી,ધારો કે $\cos 3\alpha = \frac{b}{\sqrt{a^2 + b^2}}$.તેથી $E = \frac{\sqrt{a^2 + b^2}}{\sin \alpha \cos \alpha} (\sin 3\alpha \cos \alpha - \cos 3\alpha \sin \alpha)$.$\sin(A - B) = \sin A \cos B - \cos A \sin B$ સૂત્રનો ઉપયોગ કરતા:$E = \frac{\sqrt{a^2 + b^2}}{\sin \alpha \cos \alpha} \sin(3\alpha - \alpha) = \frac{\sqrt{a^2 + b^2} \sin 2\alpha}{\sin \alpha \cos \alpha}$.$\sin 2\alpha = 2 \sin \alpha \cos \alpha$ હોવાથી:$E = \frac{\sqrt{a^2 + b^2} (2 \sin \alpha \cos \alpha)}{\sin \alpha \cos \alpha} = 2 \sqrt{a^2 + b^2}$.

જો $\theta = 3\alpha$ અને $\sin \theta = \frac{a}{\sqrt{a^2 + b^2}}$ હોય,તો $a \operatorname{cosec} \alpha - b \sec \alpha$ પદાવલિનું મૂલ્ય શોધો.

Similar Questions

$\sin^{2} \theta + \sin^{2}(\theta + 60^{\circ}) + \sin^{2}(\theta - 60^{\circ})$ નું મૂલ્ય શોધો.

$\sin^6 \theta + \cos^6 \theta + 3 \sin^2 \theta \cos^2 \theta = $

નીચેના પદનું મૂલ્ય $3(\sin^{4} \theta + \cos^{4} \theta) + 2(\sin^{6} \theta + \cos^{6} \theta) + 12\sin^{2} \theta \cos^{2} \theta$ શોધો.

$\sin 50^\circ - \sin 70^\circ + \sin 10^\circ = $

જો $\sin \alpha = \frac{8}{17}, 0 < \alpha < 90^{\circ}$ અને $\tan \beta = \frac{5}{12}, 0 < \beta < 90^{\circ}$ હોય,તો $\cos (\alpha - \beta)$ ની કિંમત શોધો.

Vedclass Test Series

Exam Paper Generator

Online Exam Module