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 = \( \dfrac{12}{5}\) 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 θ = \( \dfrac{4}{3}\) for some angle θ.

Asked by Pragya Singh | 1 year ago |  66

1 Answer

Solution :-

(i) Right answer is False

Explanation:-

The value of tan A is always less than 1.

Proof: In ΔMNC in which ∠N = 90∘,

MN = 3, NC = 4 and MC = 5

Value of tan M = \( \dfrac{4}{3}\) which is greater than.

The triangle can be formed with sides equal to 3, 4 and hypotenuse 

= 5 as it will follow the Pythagoras theorem.

MC2=MN2+NC2

52=32+42

25=9+16

25 = 25

(ii) Right answer is True

Explanation:-

sec A = \( \dfrac{12}{5}\) for some value of angle A

Let a ΔMNC in which ∠N = 90º,

MC=12k and MB=5k, where k is a positive real number.

By Pythagoras theorem we get,

MC2=MN2+NC2

(12k)2=(5k)2+NC2

NC2+25k2=144k2

NC2=119k2

Such a triangle is possible as it will follow the Pythagoras theorem.

(iii) Right answer is False

Explanation:-

cos A is the abbreviation used for the cosecant of angle A.

Abbreviation used for cosecant of angle M is cosec M. 

cos M is the abbreviation used for cosine of angle M.

(iv) Right answer is False

Explanation:-

cot A is the product of cot and A.

cot M is not the product of cot and M. It is the cotangent of ∠M.

(v) Right answer is  False

Explanation:-

sin θ = \( \dfrac{4}{3}\) for some angle θ.

sin θ = \(\dfrac{Opposite}{Hypotenuse}\)

We know that in a right angled triangle, Hypotenuse is the longest side.

sin θ will always less than 1 and it can never be \( \dfrac{4}{3}\) for any value of θ.

Answered by Abhisek | 1 year ago

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