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Trigonometric Ratios CBSE NCERT Solutions Chapter 8 Exercise 8.1 Question 11

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 = \frac{12}{5} 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 \theta =\frac{4}{3} for some angle \theta.


 

(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 = \frac{12}{5}

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 = \frac{12}{5}

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 \theta=\frac{4}{3}

sin \theta = (Side Opposite to Angle A) / (Hypotenuse) = \frac{4}{3}

 

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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