{"id":9108,"date":"2021-12-28T21:44:33","date_gmt":"2021-12-28T16:14:33","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9108"},"modified":"2021-12-28T21:50:34","modified_gmt":"2021-12-28T16:20:34","slug":"what-is-the-value-of-cosec-60-degrees","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-value-of-cosec-60-degrees\/","title":{"rendered":"What is the Value of Cosec 60 Degrees ?"},"content":{"rendered":"
The value of cosec\u00a060 degrees<\/strong> is \\(2\\over \\sqrt{3}\\)<\/strong>.<\/p>\n Proof :<\/strong><\/p>\n Consider an equilateral triangle ABC with each side of length of 2a. Each angle of \\(\\Delta\\) ABC is of 60 degrees. Let AD be the perpendicular from A on BC.<\/p>\n \\(\\therefore\\)\u00a0 \u00a0AD is the bisector of \\(\\angle\\) A and D is the mid-point of BC.<\/p>\n \\(\\therefore\\)\u00a0 \u00a0BD = DC = a and \\(\\angle\\) BAD = 30 degrees.<\/p>\n In \\(\\Delta\\) ADB, \\(\\angle\\) D is a right angle, AB = 2a and BD = a<\/p>\n By Pythagoras theorem,<\/p>\n \\(AB^2\\) = \\(AD^2\\) + \\(BD^2\\)\u00a0 \\(\\implies\\)\u00a0 \\(2a^2\\) = \\(AD^2\\) + \\(a^2\\)<\/p>\n \\(\\implies\\)\u00a0 \\(AD^2\\) = \\(4a^2\\) – \\(a^2\\) = \\(3a^2\\)\u00a0 \u00a0\\(\\implies\\)\u00a0 AD = \\(\\sqrt{3}a\\)<\/p>\n Now, In triangle ADB, \\(\\angle\\) B = 60 degrees<\/p>\n