Without using trigonometric tables, prove that

(i) \(\frac{2sin68^\circ}{cos22^\circ}-\frac{2cot15^\circ}{5tan75^\circ}- \frac{3tan45^\circ{tan20^\circ}tan40^\circ{tan50^\circ}tan70^\circ}5\) = 1

2sin68°/cos22°-2cot15°/5tan75°-3tan45°tan20°tan40°tan50°tan70°/5 = 1

(ii) \(\frac{7cos55^\circ}{3sin35^\circ}-\frac{4(cos70^\circ{cosec20^\circ})}{3(tan5​​^\circ{tan25^\circ}tan45^\circ{tan65^\circ{tan85^\circ}})}\) = 1

7cos55°/3sin35° – 4(cos70°cosec20°)/3(tan5°tan45°tan65°tan85°)

If E₁, E₂, E₃ are three mutually exclusive event and exhaustive events of an experiment such that–

 2P(E₁) = 3P(E₂) = P(E₃), then find P(E₁).