If cos⁡θ1cos⁡θ2+sin⁡θ1sin⁡θ2=cos⁡θ0cos⁡θ2+sin⁡θ0sin⁡θ2=1\frac{\cos \theta_1}{\cos \theta_2} + \frac{\sin \theta_1}{\sin \theta_2} = \frac{\cos \theta_0}{\cos \theta_2} + \frac{\sin \theta_0}{\sin \theta_2} = 1…

Mathematics

Problem

If cos⁡θ1cos⁡θ2+sin⁡θ1sin⁡θ2=cos⁡θ0cos⁡θ2+sin⁡θ0sin⁡θ2=1\frac{\cos \theta_1}{\cos \theta_2} + \frac{\sin \theta_1}{\sin \theta_2} = \frac{\cos \theta_0}{\cos \theta_2} + \frac{\sin \theta_0}{\sin \theta_2} = 1 , where θ1\theta_1 and θ0\theta_0 do not differ by an even multiple of π\pi , prove that cos⁡θ1⋅cos⁡θ0cos⁡2θ2+sin⁡θ1⋅sin⁡θ0sin⁡2θ2=−1\frac{\cos \theta_1 \cdot \cos \theta_0}{\cos^2 \theta_2} + \frac{\sin \theta_1 \cdot \sin \theta_0}{\sin^2 \theta_2} = -1

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