Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems If , where and do not differ by an even multiple of , prove that _1 _0 ^2 _2 + _1 _0…
MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry
Problem If cos θ 1 cos θ 2 + sin θ 1 sin θ 2 = cos θ 0 cos θ 2 + sin θ 0 sin θ 2 = 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 c o s θ 2 c o s θ 1 + s i n θ 2 s i n θ 1 = c o s θ 2 c o s θ 0 + s i n θ 2 s i n θ 0 = 1 θ 1 \theta_1 θ 1 θ 0 \theta_0 θ 0 π \pi π cos θ 1 ⋅ cos θ 0 cos 2 θ 2 + sin θ 1 ⋅ sin θ 0 sin 2 θ 2 = − 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 cos 2 θ 2 cos θ 1 ⋅ cos θ 0 + sin 2 θ 2 sin θ 1 ⋅ sin θ 0 = − 1 Browse the problem library