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Ex 8.4, 1 - Express sin A, sec A and tan A in terms of cot A - Ex 8.4

Ex 8.4, 1 - Chapter 8 Class 10 Introduction to Trignometry - Part 2
Ex 8.4, 1 - Chapter 8 Class 10 Introduction to Trignometry - Part 3

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Transcript

Ex 8.3, 1 Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. tan A We know that tan A = 𝟏/𝒄𝒐𝒕⁑𝑨 cosec A We know that 1 + cot2 A = cosec2 A cosec2 A = 1 + cot2 A cosec A = Β± √(1+π‘π‘œπ‘‘2 𝐴) Here, A is acute (i.e. less than 90Β°) & cosec A is positive when A is acute So, cosec A = √(1+π‘π‘œπ‘‘2 𝐴) sin A sin A = 𝟏/(𝒄𝒐𝒔𝒆𝒄 𝑨) Putting value of cosec A found above sin A = 1/(√(1 + π‘π‘œπ‘‘2 𝐴) ) Sec A We know that 1 + tan2 A = sec2 A sec2 A = 1 + tan2 A sec A = Β± √((1+π‘‘π‘Žπ‘›2 𝐴)) Here, A is acute (i.e. less than 90Β°) & sec A is positive when A is acute sec A = √((1+π‘‘π‘Žπ‘›2 𝐴)) sec A = √((1+1/(π‘π‘œπ‘‘2 𝐴))) sec A = √(((π‘π‘œπ‘‘2 𝐴 + 1)/(π‘π‘œπ‘‘2 𝐴)) ) sec A = √(π‘π‘œπ‘‘2 𝐴 + 1)/cot⁑𝐴

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.