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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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Ex 8.4, 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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