{"id":9183,"date":"2022-01-01T00:11:27","date_gmt":"2021-12-31T18:41:27","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9183"},"modified":"2022-01-01T00:38:27","modified_gmt":"2021-12-31T19:08:27","slug":"prove-that-cot90-theta-tantheta","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-cot90-theta-tantheta\/","title":{"rendered":"Prove that \\(Cot(90 – \\theta)\\) = \\(Tan\\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
tan A = \\(tan\\theta\\) = \\(BC\\over AB\\) ……..(1)<\/p>\n
cot C = \\(cot(90 – \\theta)\\) = \\(BC\\over AB\\) ……..(2)<\/p>\n
From (1) and (2), we have<\/p>\n
\\(cot(90 – \\theta)\\) = \\(tan\\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\\) tan A = \\(tan\\theta\\) = \\(BC\\over AB\\) ……..(1) cot C = \\(cot(90 – \\theta)\\) = \\(BC\\over AB\\) …<\/p>\n