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(i) The value of tan A is always less than 1.
(ii) sec A = for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) for some angle
.
Asked by Vishwa Nath Last Modified
Answer 
Tasneem
(i) Consider a ΔABC, right-angled at B.
but
Hence, the given statement is false.
(ii)
Let AC be 12k, AB will be 5k, where k is a positive integer.
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(12k)2 = (5k)2 + BC2
144k2 = 25k2 + BC2
BC2 = 119k2
BC = 10.9k
It can be observed that for given two sides AC = 12k and AB = 5k,
BC should be such that,
AC − AB < BC < AC + AB
12k − 5k < BC < 12k + 5k
7k < BC < 17 k
However, BC = 10.9k. Clearly, such a triangle is possible and hence, such value of sec A is possible.
Hence, the given statement is true.
(iii) Abbreviation used for cosecant of angle A is cosec A. And cos A is the abbreviation used for cosine of angle A.
Hence, the given statement is false.
(iv) cot A is not the product of cot and A. It is the cotangent of ∠A.
Hence, the given statement is false.
In a right-angled triangle, hypotenuse is always greater than the remaining two sides. Therefore, such value of sin θ is not possible.
Hence, the given statement is false.
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Sherine Das
Well Qualified and Certified Mathematics B.Ed(M.G Usty)Teacher with more than13 years of Experience
(i) False, since Tan A=Opp. Side/Adj. Side, if opposite side > adjacent side, then the value of Tan A >1.
(ii)True, since Sec A =Hypotenuse /Adj. Side and hypotenuse >adjacent side.
(iii) False, Cos A is used for Cosine of angle A.
(iv) False, Cot A is used for Cotangent of angle A.
(v) False, since Sin A= Opposite Side/Hypotenuse and Hypotenuse >Opp. Side.
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