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/𝐜𝐨𝐬𝑨
= 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

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.

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