Question

Which one of the following statements is/are TURE ? 

1) In a △ABC, ∠A = x°, ∠B = 3x° and ∠c = 2x° , then it is an equilateral triangle.

2) If the product of two whole numbers is 21 and their difference is 4, then the ratio of the numbers is 2 : 3. 

3) The distance between the points O (0, 0) and A (2, 3) is 5 units.

4) If \(\cfrac{cos^2θ}{1-sinθ}-\cfrac{3}{2}=0\) , then θ = 30° . (0° < θ < 90°)

Answer 1

4) If \(\cfrac{cos^2θ}{1-sinθ}-\cfrac{3}{2}=0\) , then θ = 30° . (0° < θ < 90°)

(i) is wrong as angles must be equal in equilateral triangle

(ii) a x b = 21, a - b = 4 then a + b = \( { \ \sqrt{16+4(21)} \ }={ \ \sqrt{16+84} \ }={ \ \sqrt{100} \ }\) 

a + b = 10 

∴ a = 7 , b = 3

(iii) distance between them is 5 units.

(iv) 2 cos² θ  = 3 - 3 sin θ , θ  = 30° satisfies.