Question

If a₁, a₂, a₃, .... , a_n are in A.P with common difference d ≠ 0, then the value of sin d (cosec a₁ cosec a₂ + cosec a₂ cosec a₃ + .... + cosec a_n–1 cosec a_n) will be

(a) sec a₁ – sec a_n 

(b) tan a₁ – tan a_n 

(c) cosec a₁ – cosec a_n 

(d) cot a₁ – cot a_n

Answer 1

Answer : (d) cot a₁ – cot a_n 

d = a₂ – a₁ = a₃ – a₂ = a₄ – a₃ = ..... = a_n – a_{n – 1^.} 

Now, sin d (cosec a₁ cosec a₂ + cosec a₂ cosec a₃ + ..... + cosec a_{n – 1} cosec a_n)

= cot a₁ – cot a_n