Ex 8.3, 1 - Chapter 8 Class 10 Introduction to Trignometry

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 = ± √(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