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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ 𝐴 )/(𝑠𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ 𝐴) = 𝑩π‘ͺ/𝑨𝑩 Assuming BC >𝑨𝑩 Example: Let AB = 10 cm and BC = 15 cm Hence, tan A = 𝐡𝐢/𝐴𝐡 = 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/πœπ¨π¬β‘π‘¨ = 1/((𝑆𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘‘π‘œ ∠𝐴 )/π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’) = π‘―π’šπ’‘π’π’•π’†π’π’–π’”π’†/(π‘Ίπ’Šπ’…π’† 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒕𝒐 βˆ π‘¨) 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〗 =(π’”π’Šπ’…π’† 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝑨 )/(π’”π’Šπ’…π’† π’π’‘π’‘π’π’”π’Šπ’•π’† 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 ΞΈ = 4/3 for some angle ΞΈ. sin ΞΈ = (π’”π’Šπ’…π’† π’π’‘π’‘π’π’”π’Šπ’•π’† 𝜽)/π‘―π’šπ’‘π’π’•π’†π’π’–π’”π’† Since hypotenuse is largest side, denominator will be always more than numerator . Hence, sin ΞΈ will always be always be less than 1 Thus, sin ΞΈ = 4/3 is false

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.