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 = ± √(1+𝑐𝑜𝑡2 𝐴) Here, A is acute angle (i.e. less than 90°) & cosec A is positive when A is acute ∴ cosec A = √(𝟏+𝒄𝒐𝒕𝟐 𝑨) sin A sin A = 1/(𝑐𝑜𝑠𝑒𝑐 𝐴) Putting value of cosec A found above = 𝟏/(√(𝟏 + 𝒄𝒐𝒕^𝟐 𝑨) ) sec a We know that 1 + tan2 A = sec2 A sec2 A = 1 + tan2 A sec A = ± √((1+𝑡𝑎𝑛2 𝐴)) Here, A is acute angle(i.e. less than 90°) & sec A is positive when A is acute ∴ sec A = √((1+𝑡𝑎𝑛2 𝐴)) Converting tan A to cot A = √((𝟏+𝟏/(𝒄𝒐𝒕𝟐 𝑨))) = √(((𝑐𝑜𝑡2 𝐴 + 1)/(𝑐𝑜𝑡2 𝐴)) ) = √(〖𝒄𝒐𝒕〗^𝟐⁡𝑨 + 𝟏)/𝒄𝒐𝒕⁡𝑨

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.