cos ^2 10^{circ}-cos 10^{circ} cdot cos 50^{c | vedclass

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Question

(C) ધારો કે $E = \cos ^2 10^{\circ}-\cos 10^{\circ} \cos 50^{\circ}+\cos ^2 50^{\circ}$.નિત્યસમ $\cos ^2 	heta = \frac{1+\cos 2	heta}{2}$ નો ઉપયોગ ક

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(C) ધારો કે $E = \cos ^2 10^{\circ}-\cos 10^{\circ} \cos 50^{\circ}+\cos ^2 50^{\circ}$.નિત્યસમ $\cos ^2 	heta = \frac{1+\cos 2	heta}{2}$ નો ઉપયોગ કરતા:$E = \frac{1+\cos 20^{\circ}}{2} - \cos 10^{\circ} \cos 50^{\circ} + \frac{1+\cos 100^{\circ}}{2}$$E = 1 + \frac{1}{2} \cos 20^{\circ} - \frac{1}{2} [\cos 60^{\circ} + \cos 40^{\circ}] + \frac{1}{2} \cos 100^{\circ}$$E = \frac{3}{4} + \frac{1}{2} \cos 20^{\circ} + \frac{1}{2} [\cos 100^{\circ} - \cos 40^{\circ}]$$\cos C - \cos D$ ના સૂત્રનો ઉપયોગ કરતા:$E = \frac{3}{4} + \frac{1}{2} \cos 20^{\circ} - \frac{1}{2} \cos 20^{\circ} = \frac{3}{4}$.

$\cos ^2 10^{\circ}-\cos 10^{\circ} \cdot \cos 50^{\circ}+\cos ^2 50^{\circ}$ નું મૂલ્ય શોધો.

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અંતરાલ $(0, 2\pi)$ માં સમીકરણ $\cos x \cos \left(\frac{\pi}{3}-x\right) \cos \left(\frac{\pi}{3}+x\right)=\frac{1}{4}$ ના ઉકેલોનો સરવાળો શોધો.

જો $x \sin \theta = y \sin \left( \theta + \frac{2\pi}{3} \right) = z \sin \left( \theta + \frac{4\pi}{3} \right)$ હોય,તો:

$\sqrt{3} \operatorname{cosec} 20^{\circ} - \sec 20^{\circ}$ ની કિંમત શોધો.

જો $\frac{\cos (\theta_1+\theta_2)}{\cos (\theta_1-\theta_2)}+\frac{\cos (\theta_3-\theta_4)}{\cos (\theta_3+\theta_4)}=0$ હોય,તો $\cot \theta_1 \cdot \cot \theta_2 \cdot \cot \theta_3 \cdot \cot \theta_4=$

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