State whether the following are true or false. Justify your answer:

(1) sin θ = , for some angle having measure θ.

(2) cos θ = , for some angle having measure θ.

(3) cosecA = for some measure of angle A.

(4) The value of tanA is always less than 1.

(5) secB = for some ∠B.

(6) cos θ = 100 for some angle having measure θ.

(1) No, it is false, because we know that hypotenuse is smallest side and it is the denominator which is smaller than the numerator.

IT IS FALSE.

(2) Yes, it is true, since the denominator is greater than the numerator which implies that it is possible for the hypotenuse to be the greatest side, and ∴ the triangle could be formed.

(3) Yes, it is true because the hypotenuse is the numerator in case of cosec and it is greater than denominator which means the triangle can be formed.

(4) The statement is false.

The value of tan could be greater than 1.

consider a triangle whose tan of an angle is smaller than 1, then the other angle will definitely have a tan greater than 1. because their ratios are just inversed.

(5) The statement is false, in sec ratio numerator is the hypotenuse which is the smaller than the denominator which is not possible.

(6) The Statement is False. Because here numerator is 100 and the denominator is 1, and denominator is the hypotenuse and the numerator is any of the perpendicular side, and hypotenuse is always the longest side. But here it is not so and hence it is not possible.