Trigonometric Ratios CBSE NCERT Solutions Chapter 8 Exercise 8.1 Question 11
11. State whether the following are true or false. Justify your answer.
(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) sin
for some angle
.
(i)
tan A = (Side Opposite to Angle A) / (Side Adjacent to Angle A)
Side Adjacent to Angle A can be equal to side opposite to angle A. Therefore, value of tan A can be equal to 1. Therefore, the given statement is false.
(ii)
sec A =
sec A = (Hypotenuse) / (Side Adjacent to Angle A)
As the length of the hypotenuse of triangle is always greater than the length of other two sides. So, it is possible that sec A =
Therefore, the given statement is true.
(iii)
cosec A is the abbreviation used for cosecant of angle A.
Therefore, the given statement is false.
(iv)
False
(v)
sin
sin
= (Side Opposite to Angle A) / (Hypotenuse) =
It cannot be true because length of Hypotenuse cannot be smaller than length of any other side of triangle.
Therefore, the given statement is false.
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