{"id":9182,"date":"2022-01-01T00:09:23","date_gmt":"2021-12-31T18:39:23","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9182"},"modified":"2022-01-01T00:37:17","modified_gmt":"2021-12-31T19:07:17","slug":"prove-that-tan90-theta-cottheta","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-tan90-theta-cottheta\/","title":{"rendered":"Prove that \\(Tan(90 – \\theta)\\) = \\(Cot\\theta\\)."},"content":{"rendered":"
Draw a right angled triangle ABC right angled at B.<\/p>\n
Let \\(\\angle\\) A = \\(\\theta\\), then \\(\\angle\\) C = 90 – \\(\\theta\\)<\/p>\n
cot A = \\(cot\\theta\\) = \\(AB\\over BC\\) ……..(1)<\/p>\n
tan C = \\(tan(90 – \\theta)\\) = \\(AB\\over BC\\) ……..(2)<\/p>\n
From (1) and (2), we have<\/p>\n
\\(tan(90 – \\theta)\\) = \\(cot\\theta\\)<\/p>\n","protected":false},"excerpt":{"rendered":"
Solution : Draw a right angled triangle ABC right angled at B. Let \\(\\angle\\) A = \\(\\theta\\), then \\(\\angle\\) C = 90 – \\(\\theta\\) cot A = \\(cot\\theta\\) = \\(AB\\over BC\\) ……..(1) tan C = \\(tan(90 – \\theta)\\) = \\(AB\\over BC\\) …<\/p>\n