Let in a right angled triangle, the smallest angle be θ . If a triangle formed by taking the reciprocal of its sides is also a right angled triangle, then sin θ is equal to:

Step-by-step solution

Let A = θ , then B = 90 ° - θ . Hence, a is the smallest side. Then, in ∆ A C B c 2 = a 2 + b 2 On taking reciprocal, longest side become shortest and vice versa. ⇒ 1 a 2 = 1 b 2 + 1 c 2 ⇒ b 2 c 2 a 2 = b 2 + c 2     . . . i Use a = 2 R sin A = 2 R sin θ b = 2 R sin B = 2 R sin ( 90 ° - θ ) = 2 R cos θ c = 2 R sin C = 2 sin 90 ° = 2 R Hence, by i 4 R 2 cos 2 θ · 4 R 2 4 R 2 sin 2 θ = 4 R 2 cos 2 θ + 4 R 2 ⇒ cos 2 θ =