Ex 8.1, 11 - Chapter 8 Class 10 Introduction to Trignometry (Important Question)

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Ex 8.1, 11 State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than 1. tan A = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴 )/(𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐴) = 𝑩𝑪/𝑨𝑩 Assuming BC >𝑨𝑩 Example: Let AB = 10 cm and BC = 15 cm Hence, tan A = 𝐵𝐶/𝐴𝐵 = 15/10 = 1.5 Therefore, tan A = 1.5 > 1 Hence tan A can be greater than 1 So, answer is false. Ex 8.1, 11 State whether the following are true or false. Justify your answer. (ii) sec A = 12/5 for some value of angle A. This statement is True As value of sec A > 1 Explanation sec A = 𝟏/𝐜𝐨𝐬⁡𝑨 = 1/((𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 ∠𝐴 )/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒) = 𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆/(𝑺𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒕𝒐 ∠𝑨) As Hypotenuse will be the largest side, ∴ sec A > 1 As Hypotenuse will be the largest side, ∴ sec A > 1 Ex 8.1, 11 State whether the following are true or false. Justify your answer. (iii) cos A is the abbreviation used for the cosecant of angle A. This statement is False Because cos A means cosine of angle A cosec A means cosecant of angle A Ex 8.1, 11 State whether the following are true or false. Justify your answer. (iv) cot A is the product of cot and A. This statement is False Because cot A = 1/tan⁡〖 𝐴〗 =(𝒔𝒊𝒅𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝑨 )/(𝒔𝒊𝒅𝒆 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝑨) cot A is a single term and cot without A does not have any meaning Ex 8.1, 11 State whether the following are true or false. Justify your answer. (v) sin θ = 4/3 for some angle θ. sin θ = (𝒔𝒊𝒅𝒆 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝜽)/𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 Since hypotenuse is largest side, denominator will be always more than numerator . Hence, sin θ will always be always be less than 1 Thus, sin θ = 4/3 is false